Bibliography Bibliography G Bibliography I

Bibliography H

L. Habsieger (1986) La $q$ -conjecture de Macdonald-Morris pour $G_{2}$ . C. R. Acad. Sci. Paris Sér. I Math. 303 (6), pp. 211–213 (French).
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External Links:

ISSN 0249-6291, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.14.

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L. Habsieger (1988) Une $q$ -intégrale de Selberg et Askey. SIAM J. Math. Anal. 19 (6), pp. 1475–1489.
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External Links:

ISSN 0036-1410, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§17.13.

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J. Hadamard (1896) Sur la distribution des zéros de la fonction $\zeta(s)$ et ses conséquences arithmétiques. Bull. Soc. Math. France 24, pp. 199–220 (French).
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Notes:

Reprinted in Oeuvres de Jacques Hadamard. Tomes I, pp. 189–210, Éditions du Centre National de la Recherche Scientifique, Paris, 1968.

External Links:

ISSN 0037-9484, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§25.10(i), §27.2(i).

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P. I. Hadži (1968) Computation of certain integrals that contain a probability function. Bul. Akad. Štiince RSS Moldoven 1968 (2), pp. 81–104. (errata insert) (Russian).
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External Links:

MathReview (H. A. Lauwerier)

Referenced by:

§7.14(iii).

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P. I. Hadži (1969) Certain integrals that contain a probability function and degenerate hypergeometric functions. Bul. Akad. S̆tiince RSS Moldoven 1969 (2), pp. 40–47 (Russian).
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External Links:

MathReview (Wazir Hasan Abdi)

Referenced by:

§7.14(iii).

Encodings:

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P. I. Hadži (1970) Some integrals that contain a probability function and hypergeometric functions. Bul. Akad. Štiince RSS Moldoven 1970 (1), pp. 49–62 (Russian).
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External Links:

MathReview (R. G. Langebartel)

Referenced by:

§7.14(iii).

Encodings:

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P. I. Hadži (1972) Certain sums that contain cylindrical functions. Bul. Akad. Štiince RSS Moldoven. 1972 (3), pp. 75–77, 94 (Russian).
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External Links:

MathReview (D. P. Gupta)

Referenced by:

§7.14(iii).

Encodings:

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P. I. Hadži (1973) The Laplace transform for expressions that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).
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External Links:

MathReview (L. Berg)

Referenced by:

§7.14(iii).

Encodings:

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P. I. Hadži (1975a) Certain integrals that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1975 (2), pp. 86–88, 95 (Russian).
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External Links:

MathReview (C. Tanaka)

Referenced by:

§7.14(iii).

Encodings:

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P. I. Hadži (1975b) Integrals containing the Fresnel functions $S(x)$ and $C(x)$ . Bul. Akad. Štiince RSS Moldoven. 1975 (3), pp. 48–60, 93 (Russian).
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External Links:

MathReview (J. Kaczmarski)

Referenced by:

§7.14(iii).

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P. I. Hadži (1976a) Expansions for the probability function in series of Čebyšev polynomials and Bessel functions. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
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External Links:

MathReview (V. L. Makarov)

Referenced by:

§7.14(iii).

Encodings:

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P. I. Hadži (1976b) Integrals that contain a probability function of complicated arguments. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 80–84, 96 (Russian).
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External Links:

MathReview (V. L. Makarov)

Referenced by:

§7.14(iii).

Encodings:

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P. I. Hadži (1978) Sums with cylindrical functions that reduce to the probability function and to related functions. Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).
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External Links:

MathReview (M. Lawrence Glasser)

Referenced by:

§7.14(iii).

Encodings:

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E. Hahn (1980) Asymptotik bei Jacobi-Polynomen und Jacobi-Funktionen. Math. Z. 171 (3), pp. 201–226 (German).
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External Links:

ISSN 0025-5874, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.15(i).

Encodings:

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W. Hahn (1949) Über Orthogonalpolynome, die $q$ -Differenzengleichungen genügen. Math. Nachr. 2, pp. 4–34 (German).
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External Links:

MathReview (N. J. Fine), ZentralBlatt

Referenced by:

§18.27(i).

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E. Hairer, S. P. Nørsett, and G. Wanner (1993) Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.
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Notes:

A reprinting with corrections appeared in 2000.

External Links:

ISBN 3-540-56670-8, MathReview, ZentralBlatt

Referenced by:

§3.7(v), §3.7(i).

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E. Hairer, S. P. Nørsett, and G. Wanner (2000) Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer-Verlag, Berlin.
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External Links:

ISBN 3-540-56670-8, Document, MathReview

Referenced by:

§32.17.

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E. Hairer and G. Wanner (1996) Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.
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External Links:

ISBN 3-540-60452-9, MathReview, ZentralBlatt

Referenced by:

§3.7(v).

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N. Hale and A. Townsend (2016) A fast FFT-based discrete Legendre transform. IMA J. Numer. Anal. 36 (4), pp. 1670–1684.
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External Links:

ISSN 0272-4979, Document, Link, MathReview (Denis N. Sidorov)

Referenced by:

§18.16(iii).

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B. C. Hall (2013) Quantum theory for mathematicians. Graduate Texts in Mathematics, Vol. 267, Springer, New York.
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External Links:

ISBN 978-1-4614-7115-8; 978-1-4614-7116-5, Document, Link, MathReview Entry

Referenced by:

§1.18(x).

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B. Hall (2015) Lie groups, Lie algebras, and representations. Second edition, Graduate Texts in Mathematics, Vol. 222, Springer, Cham.
ⓘ

Notes:

An elementary introduction

External Links:

ISBN 978-3-319-13466-6; 978-3-319-13467-3, Document, Link, MathReview Entry

Referenced by:

§1.2(vi).

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R. L. Hall, N. Saad, and K. D. Sen (2010) Soft-core Coulomb potentials and Heun’s differential equation. J. Math. Phys. 51 (2), pp. Art. ID 022107, 19 pages.
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External Links:

ISSN 0022-2488, Document, FullText, MathReview, ZentralBlatt

Referenced by:

§31.17(ii), §31.17(ii).

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M. H. Halley, D. Delande, and K. T. Taylor (1993) The combination of $R$ -matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr. J. Phys. B 26 (12), pp. 1775–1790.
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External Links:

ISSN 0953-4075, Document, MathReview

Referenced by:

4th item.

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A. J. S. Hamilton (2001) Formulae for growth factors in expanding universes containing matter and a cosmological constant. Monthly Notices Roy. Astronom. Soc. 322 (2), pp. 419–425.
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External Links:

Document

Referenced by:

§8.24(ii).

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J. Hammack, D. McCallister, N. Scheffner, and H. Segur (1995) Two-dimensional periodic waves in shallow water. II. Asymmetric waves. J. Fluid Mech. 285, pp. 95–122.
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External Links:

ISSN 0022-1120, Document, MathReview

Referenced by:

Figure 21.9.1, Figure 21.9.1, Figure 21.9.2, Figure 21.9.2, §21.9, Sidebar 21.SB1, Sidebar 21.SB2.

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J. Hammack, N. Scheffner, and H. Segur (1989) Two-dimensional periodic waves in shallow water. J. Fluid Mech. 209, pp. 567–589.
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External Links:

ISSN 0022-1120, Document, MathReview

Referenced by:

§21.9, Sidebar 21.SB2.

Encodings:

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H. Hancock (1958) Elliptic Integrals. Dover Publications Inc., New York.
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Notes:

Unaltered reprint of original edition published by Wiley, New York, 1917.

External Links:

MathReview Entry, ZentralBlatt

Referenced by:

§19.8(ii).

Encodings:

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R. A. Handelsman and J. S. Lew (1970) Asymptotic expansion of Laplace transforms near the origin. SIAM J. Math. Anal. 1 (1), pp. 118–130.
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External Links:

Document, MathReview (E. Riekstiņš), ZentralBlatt

Referenced by:

§2.5(iii), §2.5(ii).

Encodings:

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R. A. Handelsman and J. S. Lew (1971) Asymptotic expansion of a class of integral transforms with algebraically dominated kernels. J. Math. Anal. Appl. 35 (2), pp. 405–433.
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External Links:

Document, MathReview (E. L. Koh), ZentralBlatt

Referenced by:

§2.5(ii).

Encodings:

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S. Hanish, R. V. Baier, A. L. Van Buren, and B. J. King (1970) Tables of Radial Spheroidal Wave Functions, Vols. 1-3, Prolate, $m=0,1,2$ ; Vols. 4-6, Oblate, $m=0,1,2$ . Technical report Naval Research Laboratory, Washington, D.C..
ⓘ

Notes:

NRL Reports 7088-7093

External Links:

ZentralBlatt

Referenced by:

3rd item.

Encodings:

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E. R. Hansen (1975) A Table of Series and Products. Prentice-Hall, Englewood Cliffs, N.J..
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Notes:

Table erratum: Math. Comp. v.47 (1986), no. 176, p. 767.

External Links:

ZentralBlatt

Referenced by:

§10.23(iv), §10.44(iv), §10.60(iv), §10.65(iv), §11.10(x), §11.7(v), §12.13(ii), §13.11, §14.18(iv), §15.15, §18.18(ix), §24.14(iii), §25.11(xi), §25.8, §4.11, §4.27, §4.41, §5.16, §6.15, §7.15, §8.17(vi).

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E. W. Hansen (1985) Fast Hankel transform algorithm. IEEE Trans. Acoust. Speech Signal Process. 32 (3), pp. 666–671.
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External Links:

ISSN 0096-3518, FullText, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

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J. Happel and H. Brenner (1973) Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media. 2nd edition, Noordhoff International Publishing, Leyden.
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Notes:

The first edition was published in 1965 by Prentice-Hall. The 2nd edition was reissued in 1983 by Springer, and in 1986 by Martinus Nijhoff Publishers (Kluwer Academic Publishers Group).

External Links:

MathReview (Chia-Shun Yih), ZentralBlatt

Referenced by:

§10.73(i).

Encodings:

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G. H. Hardy, J. E. Littlewood, and G. Pólya (1967) Inequalities. 2nd edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge.
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Notes:

Reprint of the 1952 edition and reprinted in 1988.

External Links:

ISBN 0-521-35880-9, MathReview, ZentralBlatt

Referenced by:

§1.2(iv), §1.4(viii), §1.7(i), §1.7(ii), §1.7(iii), §1.7(iv), §4.5(i), §4.5(ii).

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G. H. Hardy and J. E. Littlewood (1925) Some problems of “Partitio Numerorum” (VI): Further researches in Waring’s Problem. Math. Z. 23, pp. 1–37.
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Notes:

Reprinted in Collected Papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others), Vol. I, pp. 469–505, Clarendon Press, Oxford, 1966.

External Links:

ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.13(iii).

Encodings:

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G. H. Hardy and S. Ramanujan (1918) Asymptotic formulae in combinatory analysis. Proc. London Math. Soc. (2) 17, pp. 75–115.
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Notes:

Reprinted in Ramanujan (1962, pp. 276–309).

External Links:

Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(iii).

Encodings:

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G. H. Hardy and E. M. Wright (1979) An Introduction to the Theory of Numbers. 5th edition, The Clarendon Press Oxford University Press, New York-Oxford.
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External Links:

ISBN 0-19-853170-2; 0-19-853171-0, MathReview (T. M. Apostol), ZentralBlatt

Referenced by:

§20.12(i), Ch.27.

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G. H. Hardy (1912) Note on Dr. Vacca’s series for $\gamma$ . Quart. J. Math. 43, pp. 215–216.
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External Links:

ZentralBlatt

Referenced by:

(25.2.4), (25.2.5), §25.2(ii).

Encodings:

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G. H. Hardy (1940) Ramanujan. Twelve Lectures on Subjects Suggested by His Life and Work. Cambridge University Press, Cambridge, England.
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Notes:

Reprinted by Chelsea Publishing Company, New York, 1959.

External Links:

MathReview (H. Rademacher), ZentralBlatt

Referenced by:

§27.13(iv).

Encodings:

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G. H. Hardy (1949) Divergent Series. Clarendon Press, Oxford.
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Notes:

Reprinted by the American Mathematical Society in 2000.

External Links:

MathReview (R. P. Agnew), ZentralBlatt

Referenced by:

§1.15(ii), §1.15(viii).

Encodings:

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G. H. Hardy (1952) A Course of Pure Mathematics. 10th edition, Cambridge University Press.
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Notes:

Numerous reprintings exist, including the Centenary Edition with Foreword by T. W. Körner (Cambridge Univerity Press, 2008).

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.4(ii), §1.4(iii), §1.4(iv), §1.4(v), §1.4(vi), §1.4(vii), §4.4(iii), §4.6(i), §4.6(ii).

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B. A. Hargrave and B. D. Sleeman (1977) Lamé polynomials of large order. SIAM J. Math. Anal. 8 (5), pp. 800–842.
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External Links:

Document, MathReview (F. M. Arscott), ZentralBlatt

Referenced by:

§29.16.

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B. A. Hargrave (1978) High frequency solutions of the delta wing equations. Proc. Roy. Soc. Edinburgh Sect. A 81 (3-4), pp. 299–316.
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External Links:

ISSN 0308-2105, MathReview (V. M. Babich), ZentralBlatt

Referenced by:

§29.19(ii).

Encodings:

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F. E. Harris (2000) Spherical Bessel expansions of sine, cosine, and exponential integrals. Appl. Numer. Math. 34 (1), pp. 95–98.
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External Links:

ISSN 0168-9274, Document, MathReview, ZentralBlatt

Referenced by:

§10.60(iii), §6.10(ii), §6.15.

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F. E. Harris (2002) Analytic evaluation of two-center STO electron repulsion integrals via ellipsoidal expansion. Internat. J. Quantum Chem. 88 (6), pp. 701–734.
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External Links:

Document

Referenced by:

§8.24(iii).

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J. F. Hart, E. W. Cheney, C. L. Lawson, H. J. Maehly, C. K. Mesztenyi, J. R. Rice, H. G. Thacher, Jr., and C. Witzgall (1968) Computer Approximations. SIAM Ser. in Appl. Math., John Wiley & Sons Inc., New York.
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Notes:

Reprinted by Krieger Publishing Company, 1978.

External Links:

ZentralBlatt

Referenced by:

§3.11(i), §3.11(iii), §4.47(ii), §5.23(i), §5.23(i).

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D. R. Hartree (1936) Some properties and applications of the repeated integrals of the error function. Proc. Manchester Lit. Philos. Soc. 80, pp. 85–102.
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External Links:

ZentralBlatt

Referenced by:

§7.18(iii), §7.18(iv), §7.18(v), §7.18(vi).

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Harvard University (1945) Tables of the Modified Hankel Functions of Order One-Third and of their Derivatives. Harvard University Press, Cambridge, MA.
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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

2nd item.

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A. Hasegawa (1989) Optical Solitons in Fibers. Springer-Verlag, Berlin, Germany.
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External Links:

ISBN 0387506683

Referenced by:

§22.19(iii).

Encodings:

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C. B. Haselgrove and J. C. P. Miller (1960) Tables of the Riemann Zeta Function. Royal Society Mathematical Tables, Vol. 6, Cambridge University Press, New York.
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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§25.18(i), §25.18(ii).

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C. Hastings (1955) Approximations for Digital Computers. Princeton University Press, Princeton, N.J..
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Notes:

Assisted by Jeanne T. Hayward and James P. Wong, Jr.

External Links:

MathReview (P. W. Ketchum), ZentralBlatt

Referenced by:

1st item, 1st item.

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S. P. Hastings and J. B. McLeod (1980) A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.
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External Links:

ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt

Referenced by:

§32.11(ii).

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H. J. Haubold, A. M. Mathai, and R. K. Saxena (2011) Mittag-Leffler functions and their applications. J. Appl. Math. 2011, pp. Art. ID 298628, 51 pages.
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External Links:

ISSN 1110-757X, Document, FullText, MathReview (Rudolf Gorenflo), ZentralBlatt

Referenced by:

§10.46, §10.46.

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M. Hauss (1997) An Euler-Maclaurin-type formula involving conjugate Bernoulli polynomials and an application to $\zeta(2m+1)$ . Commun. Appl. Anal. 1 (1), pp. 15–32.
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External Links:

ISSN 1083-2564, MathReview (Pavel Guerzhoy), ZentralBlatt

Referenced by:

§24.16(iii).

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M. Hauss (1998) A Boole-type Formula involving Conjugate Euler Polynomials. In Charlemagne and his Heritage. 1200 Years of Civilization and Science in Europe, Vol. 2 (Aachen, 1995), P.L. Butzer, H. Th. Jongen, and W. Oberschelp (Eds.), pp. 361–375.
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External Links:

ISBN 2-503-50674-7, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§24.16(iii).

Encodings:

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B. Hayes (2009) The higher arithmetic. American Scientist 97, pp. 364–368.
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External Links:

FullText

Referenced by:

§3.1(iv).

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V. B. Headley and V. K. Barwell (1975) On the distribution of the zeros of generalized Airy functions. Math. Comp. 29 (131), pp. 863–877.
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External Links:

FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§9.13(i).

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G. J. Heckman (1991) An elementary approach to the hypergeometric shift operators of Opdam. Invent. Math. 103 (2), pp. 341–350.
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External Links:

ISSN 0020-9910, Document, MathReview (Eric M. Opdam), ZentralBlatt

Referenced by:

§18.37(iii).

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M. Heil (1995) Numerical Tools for the Study of Finite Gap Solutions of Integrable Systems. Ph.D. Thesis, Technischen Universität Berlin.
ⓘ

Notes:

(All relevant material, plus corrections, are included in Deconinck et al. (2004).)

External Links:

ZentralBlatt

Referenced by:

§21.5(i).

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T. Helgaker, P. Jørgensen, and J. Olsen (2012) Molecular Electronic-Structure Theory. John Wiley & Sons, New York.
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Notes:

Paperback Reprint of 2004 Edition

External Links:

ISBN 9871118531471

Referenced by:

§18.39(iii).

Encodings:

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E. J. Heller, W. P. Reinhardt, and H. A. Yamani (1973) On an “equivalent quadrature” calculation of matrix elements of $(z-p^{2}/2m)^{-1}$ using an $L^{2}$ expansion technique. J. Comput. Phys. 13, pp. 536–550.
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External Links:

Document, Link

Referenced by:

§18.39(iv).

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R. S. Heller (1976) 25D Table of the First One Hundred Values of $j_{0,s}$ , $J_{1}(j_{0,s})$ , $j_{1,s}$ , $J_{0}(j_{1,s})=J_{0}(j^{\prime}_{0,s+1})$ , $j^{\prime}_{1,s}$ , $J_{1}(j^{\prime}_{1,s})$ . Technical report Department of Physics, Worcester Polytechnic Institute, Worcester, MA.
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Notes:

Ms. of six pages deposited in the UMT file

Referenced by:

8th item.

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P. W. Hemker, T. H. Koornwinder, and N. M. Temme (1993) Wavelets: mathematical preliminaries. In Wavelets: an elementary treatment of theory and applications, Ser. Approx. Decompos., Vol. 1, pp. 13–26.
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External Links:

Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

Profile Tom H. Koornwinder.

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E. Hendriksen and H. van Rossum (1986) Orthogonal Laurent polynomials. Nederl. Akad. Wetensch. Indag. Math. 48 (1), pp. 17–36.
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External Links:

ISSN 0019-3577, Document, MathReview (W. J. Thron), ZentralBlatt

Referenced by:

§18.33(v).

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P. Henrici (1974) Applied and Computational Complex Analysis. Vol. 1: Power Series—Integration—Conformal Mapping—Location of Zeros. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.
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Notes:

Reprinted in 1988.

External Links:

ISBN 0-471-37244-7, MathReview (M. Marden), ZentralBlatt

Referenced by:

§1.10(vii), §1.9(vi), Ch.3.

Encodings:

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P. Henrici (1977) Applied and Computational Complex Analysis. Vol. 2: Special Functions—Integral Transforms—Asymptotics—Continued Fractions. Wiley-Interscience [John Wiley & Sons], New York.
ⓘ

Notes:

Reprinted in 1991.

External Links:

ISBN 0-471-01525-3, MathReview (A. E. Heins), ZentralBlatt

Referenced by:

§1.11(v), Ch.3.

Encodings:

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P. Henrici (1986) Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.
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Notes:

Reprinted in 1993.

External Links:

ISBN 0-471-08703-3; 0-471-58986-1, MathReview (A. E. Heins), ZentralBlatt

Referenced by:

§1.14(v), Ch.3.

Encodings:

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J. R. Herndon (1961a) Algorithm 55: Complete elliptic integral of the first kind. Comm. ACM 4 (4), pp. 180.
ⓘ

Notes:

Includes Algol program, maximum accuracy 8D. For certification see same journal 6 (1966), pp. 166–167

External Links:

ISSN 0001-0782, Document

Referenced by:

§19.39(ii).

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J. R. Herndon (1961b) Algorithm 56: Complete elliptic integral of the second kind. Comm. ACM 4 (4), pp. 180–181.
ⓘ

Notes:

Includes Algol program, maximum accuracy 8D. For certification see same journal 9 (1966), p. 12

External Links:

ISSN 0001-0782, Document

Referenced by:

§19.39(ii).

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D. R. Herrick and S. O’Connor (1998) Inverse virial symmetry of diatomic potential curves. J. Chem. Phys. 109 (1), pp. 11–19.
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External Links:

Document

Referenced by:

§15.18.

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C. S. Herz (1955) Bessel functions of matrix argument. Ann. of Math. (2) 61 (3), pp. 474–523.
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External Links:

FullText, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§35.1, §35.2, §35.3(ii), §35.5(i), §35.5(ii), §35.5(iii), §35.6(i), §35.6(ii), §35.6(iii), §35.6(iv), §35.7(i), §35.7(ii), §35.7(iv), §35.8(i), §35.8(ii), §35.8(iv), Ch.35, Notations P.

Encodings:

BibTeX
H. W. Hethcote (1970) Error bounds for asymptotic approximations of zeros of Hankel functions occurring in diffraction problems. J. Mathematical Phys. 11 (8), pp. 2501–2504.
ⓘ

External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(xiv).

Encodings:

BibTeX
D. Hilbert (1909) Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl $n^{\mathrm{ter}}$ Potenzen (Waringsches Problem). Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, pp. 17–36 (German).
ⓘ

Notes:

Also in Math. Annalen (1909), v. 67, pp. 281–300.

External Links:

Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.13(iii).

Encodings:

BibTeX
F. B. Hildebrand (1974) Introduction to Numerical Analysis. 2nd edition, McGraw-Hill Book Co., New York.
ⓘ

Notes:

Reprinted by Dover Publications Inc., New York, 1987.

External Links:

ISBN 0-486-65363-3, MathReview, ZentralBlatt

Referenced by:

§3.3(iii), §3.3(iv), §3.3(v), §3.4(i), §3.8(v), Ch.3.

Encodings:

BibTeX
T. H. Hildebrandt (1938) Definitions of Stieltjes Integrals of the Riemann Type. Amer. Math. Monthly 45 (5), pp. 265–278.
ⓘ

External Links:

ISSN 0002-9890, Document, Link, MathReview Entry

Referenced by:

§1.16(ix).

Encodings:

BibTeX
C. J. Hill (1828) Über die Integration logarithmisch-rationaler Differentiale. J. Reine Angew. Math. 3, pp. 101–159.
ⓘ

External Links:

ZentralBlatt

Referenced by:

§25.12(i).

Encodings:

BibTeX
G. W. Hill and A. W. Davis (1973) Algorithm 442: Normal deviate. Comm. ACM 16 (1), pp. 51–52.
ⓘ

Notes:

Includes Algol program, minimum accuracy 24D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§7.25(ii).

Encodings:

BibTeX
G. W. Hill (1970) Algorithm 395: Student’s t-distribution. Comm. ACM 13 (10), pp. 617–619.
ⓘ

Notes:

Includes Algol program, maximum accuracy 11S. For Remarks see ACM Trans. Math. Software 5(1979) and 7(1981)

External Links:

ISSN 0001-0782, Document, Remark 1, Remark 2

Referenced by:

§8.28(iv).

Encodings:

BibTeX
G. W. Hill (1981) Algorithm 571: Statistics for von Mises’ and Fisher’s distributions of directions: $I_{1}(x)/I_{0}(x)$ , $I_{1.5}(x)/I_{0.5}(x)$ and their inverses [S14]. ACM Trans. Math. Software 7 (2), pp. 233–238.
ⓘ

Notes:

Single-precision Fortran, minimum accuracy 8S.

External Links:

ISSN 0098-3500, Document, GAMS (module 571; package TOMS)

Referenced by:

5th item.

Encodings:

BibTeX
I. D. Hill (1973) Algorithm AS66: The normal integral. Appl. Statist. 22 (3), pp. 424–427.
ⓘ

Notes:

Double-precision Fortran, maximum accuracy 12D.

External Links:

FullText, Code

Referenced by:

5th item.

Encodings:

BibTeX
E. Hille (1929) Note on some hypergeometric series of higher order. J. London Math. Soc. 4, pp. 50–54.
ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§16.9.

Encodings:

BibTeX
E. Hille (1976) Ordinary Differential Equations in the Complex Domain. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.
ⓘ

Notes:

Reprinted by Dover Publications Inc., New York, 1997

External Links:

ISBN 0-471-39964-7, MathReview (S. Strelitz), ZentralBlatt

Referenced by:

§16.8(i), §32.2(i).

Encodings:

BibTeX
P. Hillion (1997) Diffraction and Weber functions. SIAM J. Appl. Math. 57 (6), pp. 1702–1715.
ⓘ

External Links:

ISSN 0036-1399, Document, MathReview, ZentralBlatt

Referenced by:

§12.13(ii), §12.17.

Encodings:

BibTeX
M. H. Hirata (1975) Flow near the bow of a steadily turning ship. J. Fluid Mech. 71 (2), pp. 283–291.
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External Links:

Document, ZentralBlatt

Referenced by:

§11.12.

Encodings:

BibTeX
N. J. Hitchin (1995) Poncelet Polygons and the Painlevé Equations. In Geometry and Analysis (Bombay, 1992), Ramanan (Ed.), pp. 151–185.
ⓘ

External Links:

MathReview (Henrik Pedersen), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX
N. J. Hitchin (2003) A lecture on the octahedron. Bull. London Math. Soc. 35 (5), pp. 577–600.
ⓘ

External Links:

ISSN 0024-6093, Document, MathReview (I. Dolgachev), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX
M. Hiyama and H. Nakamura (1997) Two-center Coulomb functions. Comput. Phys. Comm. 103 (2-3), pp. 209–216.
ⓘ

Notes:

Double-precision Fortran code.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

BibTeX
E. W. Hobson (1928) A Treatise on Plane and Advanced Trigonometry. 7th edition, Cambridge University Press.
ⓘ

Notes:

Reprinted by Dover Publications Inc., New York, 2004.

External Links:

MathReview, ZentralBlatt

Referenced by:

§4.16, §4.17, §4.19, §4.2(ii), §4.2(iii), §4.21(i), §4.21(ii), §4.21(iii), §4.21(iv), §4.22, §4.23(v), §4.23(vi), §4.24(i), §4.24(iii), §4.28, §4.30, §4.31, §4.35(i), §4.35(ii), §4.35(iii), §4.35(iv), §4.42(i), §4.42(ii), §4.43, §4.8(ii), Ch.4.

Encodings:

BibTeX
E. W. Hobson (1931) The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, London-New York.
ⓘ

Notes:

Reprinted by Chelsea Publishing Company, New York, 1955 and 1965.

External Links:

ISBN 0-8284-0104-7, MathReview, ZentralBlatt

Referenced by:

§14.1, §14.11, §14.16(ii), §14.16(iii), §14.20(x), §14.27, §14.27, §14.3(i), §14.3(i), Ch.14, §29.18(iii), Ch.29.

Encodings:

BibTeX
H. Hochstadt (1963) Estimates of the stability intervals for Hill’s equation. Proc. Amer. Math. Soc. 14 (6), pp. 930–932.
ⓘ

External Links:

FullText, MathReview (P. Ungar), ZentralBlatt

Referenced by:

§28.29(iii).

Encodings:

BibTeX
H. Hochstadt (1964) Differential Equations: A Modern Approach. Holt, Rinehart and Winston, New York.
ⓘ

Notes:

Reprinted by Dover in 1975.

External Links:

MathReview (Z. Opial), ZentralBlatt

Referenced by:

§29.3(vi).

Encodings:

BibTeX
H. Hochstadt (1971) The Functions of Mathematical Physics. Wiley-Interscience [John Wiley & Sons, Inc.], New York-London-Sydney.
ⓘ

Notes:

Pure and Applied Mathematics, Vol. XXIII. Reprinted with corrections by Dover Publications Inc., New York, 1986.

External Links:

MathReview, ZentralBlatt

Referenced by:

§13.28(i), Ch.13, §15.17(ii), Ch.15.

Encodings:

BibTeX
L. E. Hoisington and G. Breit (1938) Calculation of Coulomb wave functions for high energies. Phys. Rev. 54 (8), pp. 627–628.
ⓘ

External Links:

Document

Referenced by:

§33.7.

Encodings:

BibTeX
P. Holmes and D. Spence (1984) On a Painlevé-type boundary-value problem. Quart. J. Mech. Appl. Math. 37 (4), pp. 525–538.
ⓘ

External Links:

ISSN 0033-5614, Document, MathReview, ZentralBlatt

Referenced by:

§32.11(i), §32.17.

Encodings:

BibTeX
E. Hopf (1934) Mathematical Problems of Radiative Equilibrium. Cambridge Tracts in Mathematics and Mathematical Physics No. 31, Cambridge University Press, Cambridge.
ⓘ

Notes:

Reprinted by Stechert-Hafner, Inc., New York, 1964

External Links:

MathReview, ZentralBlatt

Referenced by:

§8.19(ix), §8.24(iii).

Encodings:

BibTeX
K. Horata (1989) An explicit formula for Bernoulli numbers. Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.
ⓘ

External Links:

ZentralBlatt

Referenced by:

§24.6.

Encodings:

BibTeX
K. Horata (1991) On congruences involving Bernoulli numbers and irregular primes. II. Rep. Fac. Sci. Technol. Meijo Univ. 31, pp. 1–8.
ⓘ

External Links:

ZentralBlatt

Referenced by:

§24.15(iii).

Encodings:

BibTeX
F. T. Howard (1976) Roots of the Euler polynomials. Pacific J. Math. 64 (1), pp. 181–191.
ⓘ

External Links:

MathReview (M. Marden), ZentralBlatt

Referenced by:

§24.12(ii).

Encodings:

BibTeX
F. T. Howard (1996a) Explicit formulas for degenerate Bernoulli numbers. Discrete Math. 162 (1-3), pp. 175–185.
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External Links:

ISSN 0012-365X, Document, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.16(i).

Encodings:

BibTeX
F. T. Howard (1996b) Sums of powers of integers via generating functions. Fibonacci Quart. 34 (3), pp. 244–256.
ⓘ

External Links:

ISSN 0015-0517, MathReview (Noriaki Kimura), ZentralBlatt

Referenced by:

§24.4(iii).

Encodings:

BibTeX
C. J. Howls, P. J. Langman, and A. B. Olde Daalhuis (2004) On the higher-order Stokes phenomenon. Proc. Roy. Soc. London Ser. A 460, pp. 2285–2303.
ⓘ

External Links:

ISSN 1364-5021, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§2.11(iv).

Encodings:

BibTeX
C. J. Howls and A. B. Olde Daalhuis (1999) On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order. Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.
ⓘ

External Links:

ISSN 1364-5021, Document, MathReview (A. D. Wood), ZentralBlatt

Referenced by:

§10.20(ii).

Encodings:

BibTeX
C. J. Howls (1992) Hyperasymptotics for integrals with finite endpoints. Proc. Roy. Soc. London Ser. A 439, pp. 373–396.
ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX
M. Hoyles, S. Kuyucak, and S. Chung (1998) Solutions of Poisson’s equation in channel-like geometries. Comput. Phys. Comm. 115 (1), pp. 45–68.
ⓘ

External Links:

ISSN 0010-4655, Document, Code, MathReview Entry, ZentralBlatt

Referenced by:

§14.31(i).

Encodings:

BibTeX
Y. P. Hsu (1993) Development of a Gaussian hypergeometric function code in complex domains. Internat. J. Modern Phys. C 4 (4), pp. 805–840.
ⓘ

External Links:

ISSN 0129-1831, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§15.20(iii).

Encodings:

BibTeX
L. K. Hua (1963) Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains. Translations of Mathematical Monographs, Vol. 6, American Mathematical Society, Providence, RI.
ⓘ

Notes:

Reprinted in 1979.

External Links:

ISBN 0-8218-1556-3, MathReview, ZentralBlatt

Referenced by:

§35.4(i).

Encodings:

BibTeX
I. Huang and S. Huang (1999) Bernoulli numbers and polynomials via residues. J. Number Theory 76 (2), pp. 178–193.
ⓘ

External Links:

ISSN 0022-314X, Document, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.14(ii).

Encodings:

BibTeX
J. H. Hubbard and B. B. Hubbard (2002) Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. 2nd edition, Prentice Hall Inc., Upper Saddle River, NJ.
ⓘ

External Links:

ISBN 0-13-041408-5; 978-0-13-041408-3, MathReview (W. P. Ziemer), ZentralBlatt

Referenced by:

§1.6(i).

Encodings:

BibTeX
M. H. Hull and G. Breit (1959) Coulomb Wave Functions. In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.), pp. 408–465.
ⓘ

External Links:

MathReview (G. Källén)

Referenced by:

§33.2(iii), §33.23(vii), §33.23(vii), §33.24, §33.5(ii), §33.7, Ch.33.

Encodings:

BibTeX
T. E. Hull and A. Abrham (1986) Variable precision exponential function. ACM Trans. Math. Software 12 (2), pp. 79–91.
ⓘ

External Links:

ISSN 0098-3500, Document, MathReview Entry, ZentralBlatt

Referenced by:

§4.48(iii).

Encodings:

BibTeX
P. Humbert (1920) Sur les fonctions hypercylindriques. C. R. Acad. Sci. Paris Sér. I Math. 171, pp. 490–492 (French).
ⓘ

External Links:

ZentralBlatt

Referenced by:

§13.1, Notations P.

Encodings:

BibTeX
J. Humblet (1984) Analytical structure and properties of Coulomb wave functions for real and complex energies. Ann. Physics 155 (2), pp. 461–493.
ⓘ

External Links:

ISSN 0003-4916, Document, MathReview

Referenced by:

§33.10(ii), §33.13, §33.22(vii).

Encodings:

BibTeX
J. Humblet (1985) Bessel function expansions of Coulomb wave functions. J. Math. Phys. 26 (4), pp. 656–659.
ⓘ

External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§33.10(ii), §33.10(iii), §33.14(iv), §33.9(ii), §33.9(ii).

Encodings:

BibTeX
C. Hunter and B. Guerrieri (1981) The eigenvalues of Mathieu’s equation and their branch points. Stud. Appl. Math. 64 (2), pp. 113–141.
ⓘ

External Links:

ISSN 0022-2526, MathReview (R. C. Varma), ZentralBlatt

Referenced by:

§28.7.

Encodings:

BibTeX
C. Hunter and B. Guerrieri (1982) The eigenvalues of the angular spheroidal wave equation. Stud. Appl. Math. 66 (3), pp. 217–240.
ⓘ

External Links:

ISSN 0022-2526, MathReview, ZentralBlatt

Referenced by:

§30.9(iii).

Encodings:

BibTeX
C. Hunter (1981) Two Parametric Eigenvalue Problems of Differential Equations. In Spectral Theory of Differential Operators (Birmingham, AL, 1981), North-Holland Math. Stud., Vol. 55, pp. 233–241.
ⓘ

External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§28.7.

Encodings:

BibTeX
G. Hunter and M. Kuriyan (1976) Asymptotic expansions of Mathieu functions in wave mechanics. J. Comput. Phys. 21 (3), pp. 319–325.
ⓘ

External Links:

Document, MathReview (John P. Coleman)

Referenced by:

5th item.

Encodings:

BibTeX
A. Hurwitz (1882) Einige Eigenschaften der Dirichletschen Functionen $F(s)=\sum(\frac{D}{n})\cdot\frac{1}{n}$ , die bei der Bestimmung der Klassenanzahlen binärer quadratischer Formen auftreten. Zeitschrift für Math. u. Physik 27, pp. 86–101 (German).
ⓘ

External Links:

ZentralBlatt

Referenced by:

§25.11(i).

Encodings:

BibTeX
M. N. Huxley (2003) Exponential sums and lattice points. III. Proc. London Math. Soc. (3) 87 (3), pp. 591–609.
ⓘ

External Links:

ISSN 0024-6115, Document, Link, MathReview (Angel V. Kumchev), ZentralBlatt

Referenced by:

§27.11, §27.11, Erratum (V1.1.8) for Section 27.11.

Encodings:

BibTeX

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