Bibliography Bibliography Q Bibliography S

Bibliography R

H. Rademacher (1938) On the partition function p(n). Proc. London Math. Soc. (2) 43 (4), pp. 241–254.
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External Links:

Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(iii).

Encodings:

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H. Rademacher (1973) Topics in Analytic Number Theory. Springer-Verlag, New York.
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Notes:

Edited by E. Grosswald, J. Lehner and M. Newman, Die Grundlehren der mathematischen Wissenschaften, Band 169

External Links:

MathReview (H. Halberstam), ZentralBlatt

Referenced by:

§1.8(iv), §20.7(viii), §20.7(viii), Ch.24.

Encodings:

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H. A. Ragheb, L. Shafai, and M. Hamid (1991) Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric. IEEE Trans. Antennas and Propagation 39 (2), pp. 218–223.
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Document

Referenced by:

6th item.

Encodings:

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M. Rahman (1981) A non-negative representation of the linearization coefficients of the product of Jacobi polynomials. Canad. J. Math. 33 (4), pp. 915–928.
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External Links:

ISSN 0008-414X, Document, Link, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.18(v).

Encodings:

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M. Rahman (2001) The Associated Classical Orthogonal Polynomials. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 255–279.
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External Links:

MathReview (Wadim Zudilin), ZentralBlatt

Referenced by:

§18.30(viii).

Encodings:

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E. M. Rains (1998) Normal limit theorems for symmetric random matrices. Probab. Theory Related Fields 112 (3), pp. 411–423.
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External Links:

ISSN 0178-8051, Document, MathReview (Alexei Khorunzhy), ZentralBlatt

Referenced by:

§35.9.

Encodings:

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E. D. Rainville (1960) Special Functions. The Macmillan Co., New York.
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External Links:

MathReview (R. Hamming), ZentralBlatt

Referenced by:

§14.7(iv), §16.3(ii), §16.3(ii), §16.4(iii), (18.12.2_5), §18.12, §18.9(ii).

Encodings:

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A. Ralston (1965) Rational Chebyshev approximation by Remes’ algorithms. Numer. Math. 7 (4), pp. 322–330.
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External Links:

ISSN 0029-599X, Document, MathReview (C. W. Clenshaw), ZentralBlatt

Referenced by:

§3.11(i).

Encodings:

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S. Ramanujan (1921) Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.
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External Links:

ISSN 0025-5874, ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(v).

Encodings:

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S. Ramanujan (1927) Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,
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Referenced by:

§24.7(i).

Encodings:

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S. Ramanujan (1962) Collected Papers of Srinivasa Ramanujan. Chelsea Publishing Co., New York.
ⓘ

Notes:

Reprinted with commentary by Bruce Berndt, AMS Chelsea Publishing Series, American Mathematical Society (2000).

External Links:

ISBN 0-8218-2076-1

Referenced by:

§8.11(v), G. H. Hardy and S. Ramanujan (1918).

Encodings:

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Ju. M. Rappoport (1979) Tablitsy modifitsirovannykh funktsii Besselya $K_{\frac{1}{2}+i\beta}(x)$ . “Nauka”, Moscow (Russian).
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Notes:

In Russian. Translated title: Tables of Modified Bessel Functions $K_{\frac{1}{2}+i\beta}(x)$

External Links:

MathReview, ZentralBlatt

Referenced by:

2nd item.

Encodings:

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Yu. L. Ratis and P. Fernández de Córdoba (1993) A code to calculate (high order) Bessel functions based on the continued fractions method. Comput. Phys. Comm. 76 (3), pp. 381–388.
ⓘ

Notes:

Double-precision Fortran, maximum accuracy 18D.

External Links:

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

Referenced by:

6th item.

Encodings:

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J. T. Ratnanather, J. H. Kim, S. Zhang, A. M. J. Davis, and S. K. Lucas (2014) Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions. ACM Trans. Math. Softw. 40 (2), pp. 14:1–14:12.
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External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

§10.74(vii), §10.74(vii), 7th item, §10.77(ix).

Encodings:

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H. E. Rauch and A. Lebowitz (1973) Elliptic Functions, Theta Functions, and Riemann Surfaces. The Williams & Wilkins Co., Baltimore, MD.
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External Links:

MathReview (H. H. Martens), ZentralBlatt

Referenced by:

§20.11(iv), §20.12(ii).

Encodings:

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J. Raynal (1979) On the definition and properties of generalized $6$ - $j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.
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External Links:

ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

Encodings:

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M. Razaz and J. L. Schonfelder (1980) High precision Chebyshev expansions for Airy functions and their derivatives. Technical report University of Birmingham Computer Centre.
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Referenced by:

3rd item.

Encodings:

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M. Razaz and J. L. Schonfelder (1981) Remark on Algorithm 498: Airy functions using Chebyshev series approximations. ACM Trans. Math. Software 7 (3), pp. 404–405.
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External Links:

ISSN 0098-3500, Document

Referenced by:

1st item.

Encodings:

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REDUCE (free interactive system)
ⓘ

Notes:

Symbolic and extended-precision general purpose computer algebra system.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index.

Encodings:

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I. S. Reed, D. W. Tufts, X. Yu, T. K. Truong, M. T. Shih, and X. Yin (1990) Fourier analysis and signal processing by use of the Möbius inversion formula. IEEE Trans. Acoustics, Speech, Signal Processing 38, pp. 458–470.
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External Links:

ZentralBlatt

Referenced by:

§27.17.

Encodings:

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M. Reed and B. Simon (1975) Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness. Academic Press, New York.
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External Links:

ISBN 978-0-12-585002-5, MathReview Entry

Referenced by:

§1.18(x).

Encodings:

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M. Reed and B. Simon (1978) Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.
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External Links:

ISBN 0-12-585004-2(vol.4), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

Encodings:

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M. Reed and B. Simon (1979) Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory. Academic Press, New York.
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External Links:

ISBN 0-12-585003-4 (vol.3), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

Encodings:

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M. Reed and B. Simon (1980) Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis. Elsevier, New York.
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Notes:

revised and expanded Edition from 1972,

External Links:

ISBN 10: 0-12-585050-6(vol. 1), MathReview Entry

Referenced by:

§1.18(x).

Encodings:

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W. H. Reid (1972) Composite approximations to the solutions of the Orr-Sommerfeld equation. Studies in Appl. Math. 51, pp. 341–368.
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External Links:

MathReview (E. A. Boyd), ZentralBlatt

Referenced by:

(9.13.25), (9.13.26), (9.13.28), (9.13.29), (9.13.32), (9.13.33), (9.13.34), §9.13(ii), §9.13(ii).

Encodings:

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W. H. Reid (1974a) Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow. Studies in Appl. Math. 53, pp. 91–110.
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External Links:

MathReview (T. W. Kao), ZentralBlatt

Referenced by:

§2.8(iii).

Encodings:

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W. H. Reid (1974b) Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. II. The general theory. Studies in Appl. Math. 53, pp. 217–224.
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External Links:

MathReview (T. W. Kao), ZentralBlatt

Referenced by:

§2.8(iii).

Encodings:

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W. H. Reid (1995) Integral representations for products of Airy functions. Z. Angew. Math. Phys. 46 (2), pp. 159–170.
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External Links:

ISSN 0044-2275, Document, MathReview (P. K. Banerji), ZentralBlatt

Referenced by:

§9.11(iii), §9.11(v), §9.11(v), (9.5.6), §9.5(ii).

Encodings:

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W. H. Reid (1997a) Integral representations for products of Airy functions. II. Cubic products. Z. Angew. Math. Phys. 48 (4), pp. 646–655.
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External Links:

ISSN 0044-2275, Document, MathReview (E. R. Love), ZentralBlatt

Referenced by:

(9.11.16), (9.11.17), §9.11(iii), §9.11(v).

Encodings:

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W. H. Reid (1997b) Integral representations for products of Airy functions. III. Quartic products. Z. Angew. Math. Phys. 48 (4), pp. 656–664.
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External Links:

ISSN 0044-2275, Document, MathReview (E. R. Love), ZentralBlatt

Referenced by:

§9.11(iii), §9.11(v).

Encodings:

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W. P. Reinhardt (2018) Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
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Notes:

arXiv:1812.02196

Referenced by:

§18.40(ii).

Encodings:

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W. P. Reinhardt (2021a) Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (4), pp. 91.
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External Links:

ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

Encodings:

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W. P. Reinhardt (2021b) Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (3), pp. 56–64.
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External Links:

ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

Encodings:

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W. Reinhardt (1982) Complex Coordinates in the Theory of Atomic and Molecular Structure and Dynamics. Annual Review of Physical Chemistry 33, pp. 223–255.
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Referenced by:

§1.18(viii).

Encodings:

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K. Reinsch and W. Raab (2000) Elliptic Integrals of the First and Second Kind – Comparison of Bulirsch’s and Carlson’s Algorithms for Numerical Calculation. In Special Functions (Hong Kong, 1999), C. Dunkl, M. Ismail, and R. Wong (Eds.), pp. 293–308.
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External Links:

MathReview, ZentralBlatt

Referenced by:

§19.36(i), §19.36(ii).

Encodings:

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F. E. Relton (1965) Applied Bessel Functions. Dover Publications Inc., New York.
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Notes:

Reprint of original Blackie & Son Limited, London, 1946.

External Links:

MathReview, ZentralBlatt

Referenced by:

§10.73(iii).

Encodings:

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G. F. Remenets (1973) Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral. Ž. Vyčisl. Mat. i Mat. Fiz. 13, pp. 1415–1424, 1636.
ⓘ

Notes:

English translation in U.S.S.R. Computational Math. and Math. Phys. 13(6), pp. 58–67

External Links:

ISSN 0044-4669, Document, MathReview (H. Zegeling), ZentralBlatt

Referenced by:

§10.74(iii).

Encodings:

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E. Ya. Remez (1957) General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.
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Notes:

English translation, AEC-TR-4491, United States Atomic Energy Commission

External Links:

MathReview (A. S. Householder)

Referenced by:

§3.11(iii).

Encodings:

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S. R. Rengarajan and J. E. Lewis (1980) Mathieu functions of integral orders and real arguments. IEEE Trans. Microwave Theory Tech. 28 (3), pp. 276–277.
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Notes:

Includes Fortran program

External Links:

FullText

Referenced by:

§28.36(ii), §28.36(iii).

Encodings:

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R. Reynolds and A. Stauffer (2021) Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function. Mathematics 9 (16).
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External Links:

Link, ISSN 2227-7390, Document

Referenced by:

§8.15.

Encodings:

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P. Ribenboim (1979) 13 Lectures on Fermat’s Last Theorem. Springer-Verlag, New York.
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External Links:

ISBN 0-387-90432-8, MathReview (T. Metsänkylä), ZentralBlatt

Referenced by:

§24.10(iv), §24.17(iii).

Encodings:

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S. O. Rice (1954) Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills. Bell System Tech. J. 33, pp. 417–504.
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External Links:

MathReview (J. Shmoys)

Referenced by:

§12.17.

Encodings:

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D. St. P. Richards (Ed.) (1992) Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications. Contemporary Mathematics, Vol. 138, American Mathematical Society, Providence, RI.
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External Links:

ISBN 0-8218-5159-4, MathReview, ZentralBlatt

Referenced by:

Ch.35, Profile Donald St. P. Richards.

Encodings:

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D. St. P. Richards (2004) Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.
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External Links:

ISSN 0022-4715, Document, MathReview (Stamatis Koumandos), ZentralBlatt

Referenced by:

§35.9.

Encodings:

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È. Ya. Riekstynš (1991) Asymptotics and Bounds of the Roots of Equations (Russian). Zinatne, Riga.
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External Links:

ISBN 5-7966-0570-4, MathReview (Guillermo López Lagomasino), ZentralBlatt

Referenced by:

§12.11(ii), §6.13.

Encodings:

BibTeX
B. Riemann (1859) Über die Anzahl der Primzahlen unter einer gegebenen Grösse. Monats. Berlin Akad. November 1859, pp. 671–680.
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Notes:

Reprinted in Gesammelte Mathematische Werke, pp. 145–155, published by Dover Publications, New York, N.Y. 1953.

Referenced by:

§25.1, (25.2.1), §25.2(i).

Encodings:

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B. Riemann (1899) Elliptische Functionen. Teubner, Leipzig.
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Notes:

Based on notes of lectures by B. Riemann edited and published by H. Stahl. Reprinted by UMI Books on Demand (Ann Arbor, MI, USA).

External Links:

ZentralBlatt

Referenced by:

§20.12(ii).

Encodings:

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B. Riemann (1851) Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse. Inauguraldissertation, Göttingen.
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Referenced by:

§21.7(i).

Encodings:

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F. Riesz and B. Sz.-Nagy (1990) Functional analysis. Dover Books on Advanced Mathematics, Dover Publications, Inc., New York.
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Notes:

Translated from the second French edition by Leo F. Boron, Reprint of the 1955 original

External Links:

ISBN 0-486-66289-6, MathReview Entry

Referenced by:

§1.18(i), §1.4(v), §1.4(v).

Encodings:

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J. Riordan (1958) An Introduction to Combinatorial Analysis. John Wiley & Sons Inc., New York.
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Notes:

Reprinted by Princeton University Press, Princeton, NJ, 1980 and reissued by Dover Publications Inc., New York, 2002.

External Links:

MathReview (L. Moser), ZentralBlatt

Referenced by:

§1.4(iii), §26.14(ii), §26.18, §26.3(ii), §26.3(iii), Ch.26.

Encodings:

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J. Riordan (1979) Combinatorial Identities. Robert E. Krieger Publishing Co., Huntington, NY.
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Notes:

Reprint of the 1968 original with corrections.

External Links:

ISBN 0-88275-829-2, MathReview

Referenced by:

§24.5(iii), §26.5(iii), §26.8(i), §26.8(iv), §26.8(v).

Encodings:

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RISC Combinatorics Group (website) Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.
ⓘ

Notes:

Software packages for hypergeometric and $q$ -hypergeometric summation, sequences and power series, permutation groups, partition analysis, and difference equations.

External Links:

RISC Combinatorics Group

Referenced by:

6th item.

Encodings:

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S. Ritter (1998) On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators. Z. Angew. Math. Mech. 78 (1), pp. 66–72.
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External Links:

ISSN 0044-2267, Document, MathReview Entry, ZentralBlatt

Referenced by:

§29.20(ii).

Encodings:

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T. J. Rivlin (1969) An Introduction to the Approximation of Functions. Blaisdell Publishing Co. (Ginn and Co.), Waltham, MA-Toronto-London.
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Notes:

Corrected reprint by Dover Publications, Inc., New York, 1981

External Links:

ISBN 0-486-64069-8, MathReview (E. W. Cheney), ZentralBlatt

Referenced by:

§18.38(i).

Encodings:

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L. Robin (1957) Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome I. Gauthier-Villars, Paris.
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Notes:

Préface de H. Villat

External Links:

MathReview (R. Campbell), ZentralBlatt

Referenced by:

Ch.14.

Encodings:

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L. Robin (1958) Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome II. Gauthier-Villars, Paris.
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External Links:

MathReview (R. Campbell), ZentralBlatt

Referenced by:

Ch.14.

Encodings:

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L. Robin (1959) Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome III. Collection Technique et Scientifique du C. N. E. T. Gauthier-Villars, Paris.
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External Links:

MathReview (R. Campbell), ZentralBlatt

Referenced by:

Ch.14.

Encodings:

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H. P. Robinson (1972) Roots of $\tan x=x$ .
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Notes:

10 typewritten pages deposited in the UMT file at Lawrence Berkeley Laboratory, University of California, Berkeley, CA.

Referenced by:

§4.46.

Encodings:

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M. Robnik (1980) An extremum property of the $n$ -dimensional sphere. J. Phys. A 13 (10), pp. L349–L351.
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External Links:

ISSN 0305-4470, Document, MathReview

Referenced by:

§5.19(iii).

Encodings:

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D. L. Rod and B. D. Sleeman (1995) Complexity in spatio-temporal dynamics. Proc. Roy. Soc. Edinburgh Sect. A 125 (5), pp. 959–974.
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External Links:

ISSN 0308-2105, MathReview (Richard C. Churchill), ZentralBlatt

Referenced by:

§31.14(ii).

Encodings:

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M. D. Rogers (2005) Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
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External Links:

ISSN 0022-2488, Document, MathReview (Wolfgang zu Castell), ZentralBlatt

Referenced by:

§10.23(ii).

Encodings:

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S. Roman (1984) The umbral calculus. Pure and Applied Mathematics, Vol. 111, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York.
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External Links:

ISBN 0-12-594380-6, MathReview (R. Askey)

Referenced by:

§18.2(xii).

Encodings:

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V. Romanovski (1929) Sur quelques classes nouvelles de polynômes orthogonaux. C. R. Acad. Sci. Paris 188, pp. 1023–1025.
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External Links:

ZentralBlatt

Referenced by:

(18.34.5_5).

Encodings:

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A. Ronveaux (Ed.) (1995) Heun’s Differential Equations. The Clarendon Press Oxford University Press, New York.
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External Links:

ISBN 0-19-859695-2, MathReview (Harold Exton), ZentralBlatt

Referenced by:

§31.1, §31.12, §31.13, §31.2(v), §31.2(i), §31.2(iv), §31.3(ii), §31.4, §31.7(ii), §31.9(i), Ch.31, Profile Gerhard Wolf.

Encodings:

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C. C. J. Roothaan and S. Lai (1997) Calculation of $3n$ - $j$ symbols by Labarthe’s method. International Journal of Quantum Chemistry 63 (1), pp. 57–64.
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External Links:

Document

Referenced by:

§34.13.

Encodings:

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G. M. Roper (1951) Some Applications of the Lamé Function Solutions of the Linearised Supersonic Flow Equations. Technical Reports and Memoranda Technical Report 2865, Aeronautical Research Council (Great Britain).
ⓘ

Notes:

Reprinted by Her Majesty’s Stationery Office, London, 1962.

External Links:

MathReview (P. Germain)

Referenced by:

§29.19(ii).

Encodings:

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R. R. Rosales (1978) The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent. Proc. Roy. Soc. London Ser. A 361, pp. 265–275.
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External Links:

FullText, MathReview (A. D. Brjuno), ZentralBlatt

Referenced by:

§32.11(ii), §32.17, §32.3(ii).

Encodings:

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K. H. Rosen, J. G. Michaels, J. L. Gross, J. W. Grossman, and D. R. Shier (Eds.) (2000) Handbook of Discrete and Combinatorial Mathematics. CRC Press, Boca Raton, FL.
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External Links:

ISBN 0-8493-0149-1, MathReview, ZentralBlatt

Referenced by:

§26.1, §26.1, §26.11, §26.19, Ch.26, Notations, Notations.

Encodings:

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K. H. Rosen (2004) Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.
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External Links:

ISBN 0-201-87073-8, MathReview (Norman J. Richert)

Referenced by:

§27.17.

Encodings:

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P. A. Rosenberg and L. P. McNamee (1976) Precision controlled trigonometric algorithms. Appl. Math. Comput. 2 (4), pp. 335–352.
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External Links:

Document, MathReview (Luciano Biasini), ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

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H. Rosengren (1999) Another proof of the triple sum formula for Wigner $9j$ -symbols. J. Math. Phys. 40 (12), pp. 6689–6691.
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External Links:

ISSN 0022-2488, Document, MathReview (Michael Wüstner), ZentralBlatt

Referenced by:

§34.6.

Encodings:

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H. Rosengren (2004) Elliptic hypergeometric series on root systems. Adv. Math. 181 (2), pp. 417–447.
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External Links:

ISSN 0001-8708, Document, MathReview, ZentralBlatt

Referenced by:

§20.11(iii).

Encodings:

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J. B. Rosser (1939) The $n$ -th prime is greater than $n\log n$ . Proceedings of the London Mathematical Society 45, pp. 21–44.
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External Links:

Document, ZentralBlatt

Referenced by:

§27.12.

Encodings:

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G. Rota, D. Kahaner, and A. Odlyzko (1973) On the foundations of combinatorial theory. VIII. Finite operator calculus. J. Math. Anal. Appl. 42, pp. 684–760.
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External Links:

ISSN 0022-247X, Document, Link, MathReview (P. Saphar), ZentralBlatt

Referenced by:

§18.2(xii).

Encodings:

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G. Rota (1964) On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2, pp. 340–368.
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External Links:

Document, MathReview (M. A. Harrison), ZentralBlatt

Referenced by:

§27.5.

Encodings:

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M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr. (1959) The $3$ - $j$ and $6$ - $j$ Symbols. The Technology Press, MIT, Cambridge, MA.
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External Links:

ISBN 0-262-18004-9

Referenced by:

(34.1.1), §34.1, §34.1, §34.14, Erratum (V1.0.14) for Section 34.1, Erratum (V1.0.15) for Section 34.1.

Encodings:

BibTeX
M. Rothman (1954a) Tables of the integrals and differential coefficients of ${\rm Gi}(+x)$ and ${\rm Hi}(-x)$ . Quart. J. Mech. Appl. Math. 7 (3), pp. 379–384.
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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

(9.12.30), (9.12.31), §9.12(viii), §9.16, 2nd item.

Encodings:

BibTeX
M. Rothman (1954b) The problem of an infinite plate under an inclined loading, with tables of the integrals of $\rm{Ai}(\pm x)$ and $\rm{Bi}(\pm x)$ . Quart. J. Mech. Appl. Math. 7 (1), pp. 1–7.
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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§9.16, 1st item.

Encodings:

BibTeX
K. Rottbrand (2000) Finite-sum rules for Macdonald’s functions and Hankel’s symbols. Integral Transform. Spec. Funct. 10 (2), pp. 115–124.
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External Links:

ISSN 1065-2469, Document, MathReview, ZentralBlatt

Referenced by:

§10.60(iii).

Encodings:

BibTeX
D. H. Rouvray (1995) Combinatorics in Chemistry. In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.), pp. 1955–1981.
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External Links:

MathReview (Haruo Hosoya), ZentralBlatt

Referenced by:

§26.20.

Encodings:

BibTeX
C. H. Rowe (1931) A proof of the asymptotic series for log $\Gamma(z)$ and log $\Gamma{(z+a)}$ . Ann. of Math. (2) 32 (1), pp. 10–16.
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External Links:

ISSN 0003-486X, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§5.11(i).

Encodings:

BibTeX
R. Roy (2011) Sources in the development of mathematics. Cambridge University Press, Cambridge.
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Notes:

Infinite Series and Products from the Fifteenth to the Twenty-first Century

External Links:

ISBN 978-0-521-11470-7, Document, Link, MathReview (Mehdi Hassani), ZentralBlatt

Referenced by:

Profile Ranjan Roy.

Encodings:

BibTeX
R. Roy (2017) Elliptic and modular functions from Gauss to Dedekind to Hecke. Cambridge University Press, Cambridge.
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External Links:

ISBN 978-1-107-15938-9, Document, Link, MathReview (Paul M. Jenkins), ZentralBlatt

Referenced by:

Profile Ranjan Roy.

Encodings:

BibTeX
W. Rudin (1966) Real and complex analysis. McGraw-Hill Book Co., New York-Toronto, Ont.-London.
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External Links:

MathReview (R. E. Edwards)

Referenced by:

§1.2(v), §1.4(v), §1.5(v).

Encodings:

BibTeX
W. Rudin (1973) Functional Analysis. McGraw-Hill Book Co., New York.
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Notes:

McGraw-Hill Series in Higher Mathematics

External Links:

MathReview (F. Smithies), ZentralBlatt

Referenced by:

§1.18(x), §2.6(i).

Encodings:

BibTeX
W. Rudin (1976) Principles of Mathematical Analysis. 3rd edition, McGraw-Hill Book Co., New York.
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Notes:

International Series in Pure and Applied Mathematics

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.4(iii).

Encodings:

BibTeX
Hans-J. Runckel (1971) On the zeros of the hypergeometric function. Math. Ann. 191 (1), pp. 53–58.
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External Links:

ISSN 0025-5831, Document, MathReview (R. C. Varma), ZentralBlatt

Referenced by:

§15.13.

Encodings:

BibTeX
J. Rushchitsky and S. Rushchitska (2000) On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.
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External Links:

ISBN 3-7643-6287-1, MathReview Entry, ZentralBlatt

Referenced by:

5th item.

Encodings:

BibTeX
A. Russell (1909) The effective resistance and inductance of a concentric main, and methods of computing the $\mathrm{ber}$ and $\mathrm{bei}$ and allied functions. Philos. Mag. (6) 17, pp. 524–552.
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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iii).

Encodings:

BibTeX
H. Rutishauser (1957) Der Quotienten-Differenzen-Algorithmus. Mitteilungen aus dem Institut für Angewandte Mathematik an der Eidgenössischen Technischen Hochschule in Zürich, No. 7, Birkhäuser, Basel/Stuttgart (German).
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External Links:

MathReview (G. E. Forsythe), ZentralBlatt

Referenced by:

§3.10(ii).

Encodings:

BibTeX
G. B. Rybicki (1989) Dawson’s integral and the sampling theorem. Computers in Physics 3 (2), pp. 85–87.
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Referenced by:

§7.25(vi).

Encodings:

BibTeX
J. Rys, M. Dupuis, and H. F. King (1983) Computation of electron repulsion integrals using the Rys quadrature method. J. Comput. Chem. 4 (2), pp. 154–175.
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External Links:

Link

Referenced by:

§18.32, §18.39(iii).

Encodings:

BibTeX

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