Y. Takei (1995)On the connection formula for the first Painlevé equation—from the viewpoint of the exact WKB analysis.
Sūrikaisekikenkyūsho Kōkyūroku (931), pp. 70–99.
ⓘ
Notes:
Painlevé functions and asymptotic analysis (Japanese)
(Kyoto, 1995)
A. Takemura (1984)Zonal Polynomials.
Institute of Mathematical Statistics Lecture Notes—Monograph
Series, 4, Institute of Mathematical Statistics, Hayward, CA.
N. M. Temme and J. L. López (2001)The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis.
J. Comput. Appl. Math.133 (1-2), pp. 623–633.
N. M. Temme (1979a)An algorithm with ALGOL 60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives.
J. Comput. Phys.32 (2), pp. 270–279.
N. M. Temme (1987)On the computation of the incomplete gamma functions for large values of the parameters.
In Algorithms for approximation (Shrivenham, 1985),
Inst. Math. Appl. Conf. Ser. New Ser., Vol. 10, pp. 479–489.
N. M. Temme (1990b)Uniform asymptotic expansions of a class of integrals in terms of modified Bessel functions, with application to confluent hypergeometric functions.
SIAM J. Math. Anal.21 (1), pp. 241–261.
N. M. Temme (1994b)Computational aspects of incomplete gamma functions with large complex parameters.
In Approximation and Computation. A Festschrift in Honor
of Walter Gautschi, R. V. M. Zahar (Ed.),
International Series of Numerical Mathematics, Vol. 119, pp. 551–562.
N. M. Temme (1994c)Steepest descent paths for integrals defining the modified Bessel functions of imaginary order.
Methods Appl. Anal.1 (1), pp. 14–24.
N. M. Temme (1996a)Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters.
Methods Appl. Anal.3 (3), pp. 335–344.
N. M. Temme (1978)The numerical computation of special functions by use of quadrature rules for saddle point integrals. II. Gamma functions, modified Bessel functions and parabolic cylinder functions.
Report TW 183/78
Mathematisch Centrum, Amsterdam, Afdeling Toegepaste
Wiskunde.
N.M. Temme and E.J.M. Veling (2022)Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a, b and z.
Indagationes Mathematicae.
N. M. Temme (2022)Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters.
Integral Transforms Spec. Funct.33 (1), pp. 16–31.
A. Terras (1999)Fourier Analysis on Finite Groups and Applications.
London Mathematical Society Student Texts, Vol. 43, Cambridge University Press, Cambridge.
S. A. Teukolsky (1972)Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations.
Phys. Rev. Lett.29 (16), pp. 1114–1118.
I. J. Thompson and A. R. Barnett (1985)COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments.
Comput. Phys. Comm.36 (4), pp. 363–372.
ⓘ
Notes:
Double-precision Fortran, minimum accuracy: 14D. See also
Thompson (2004)
I. J. Thompson and A. R. Barnett (1987)Modified Bessel functions and of real order and complex argument, to selected accuracy.
Comput. Phys. Comm.47 (2-3), pp. 245–257.
ⓘ
Notes:
For erratum see same journal 159 (2004), no. 3, p. 243.
Double-precision Fortran, accuracy 24S, but can be increased.
I. J. Thompson (2004)Erratum to “COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments”.
Comput. Phys. Comm.159 (3), pp. 241–242.
W. J. Thompson (1994)Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems.
A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
ⓘ
Notes:
With 1 Macintosh floppy disk (3.5 inch; DD).
Programs for the calculation of symbols
are included.
W. J. Thompson (1997)Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners.
John Wiley & Sons Inc., New York.
ⓘ
Notes:
With CD-ROM containing a large collection of mathematical function software
written in Fortran 90 and Mathematica (an edition with the same software in C and Mathematica exists also).
The functions are computed for real variables only. Maximum accuracy 12D.
E. C. Titchmarsh (1958)Eigenfunction Expansions Associated with Second Order Differential Equations, Part 2, Partial Differential Equations.
Clarendon Press, Oxford.
E. C. Titchmarsh (1986a)Introduction to the Theory of Fourier Integrals.
Third edition, Chelsea Publishing Co., New York.
ⓘ
Notes:
Original edition was published in 1937 by Oxford University Press. Expanded bibliography and some improvements were made for the second and third editions.
T. Ton-That, K. I. Gross, D. St. P. Richards, and P. J. Sally (Eds.) (1995)Representation Theory and Harmonic Analysis.
Contemporary Mathematics, Vol. 191, American Mathematical Society, Providence, RI.
ⓘ
Notes:
Papers from the conference held in honor of Ray A. Kunze at
the AMS Special Session, Cincinnati, Ohio, January 12–14,
1994
Go. Torres-Vega, J. D. Morales-Guzmán, and A. Zúñiga-Segundo (1998)Special functions in phase space: Mathieu functions.
J. Phys. A31 (31), pp. 6725–6739.
C. A. Tracy and H. Widom (1997)On exact solutions to the cylindrical Poisson-Boltzmann equation with applications to polyelectrolytes.
Phys. A244 (1-4), pp. 402–413.
J. F. Traub (1964)Iterative Methods for the Solution of Equations.
Prentice-Hall Series in Automatic Computation, Prentice-Hall Inc., Englewood Cliffs, N.J..
A. Trellakis, A. T. Galick, and U. Ravaioli (1997)Rational Chebyshev approximation for the Fermi-Dirac integral .
Solid–State Electronics41 (5), pp. 771–773.
C. L. Tretkoff and M. D. Tretkoff (1984)Combinatorial Group Theory, Riemann Surfaces and Differential Equations.
In Contributions to Group Theory,
Contemp. Math., Vol. 33, pp. 467–519.
C. Truesdell (1948)An Essay Toward a Unified Theory of Special Functions.
Annals of Mathematics Studies, no. 18, Princeton University Press, Princeton, N.J..
P.-H. Tseng and T.-C. Lee (1998)Numerical evaluation of exponential integral: Theis well function approximation.
Journal of Hydrology205 (1-2), pp. 38–51.
F. Tu and Y. Yang (2013)Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves.
Trans. Amer. Math. Soc.365 (12), pp. 6697–6729.
S. A. Tumarkin (1959)Asymptotic solution of a linear nonhomogeneous second order differential equation with a transition point and its application to the computations of toroidal shells and propeller blades.
J. Appl. Math. Mech.23, pp. 1549–1565.
