hypergeometric functions of matrix argument

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21: Bibliography C

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Bessel functions $J_{\nu }(x)$ and $Y_{\nu }(x)$ of real order and real argument. Comput. Phys. Comm. 18 (1), pp. 133–142.

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Double-precision Fortran, maximum accuracy 16S.

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ISSN 0010-4655, Document, Code

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4th item.

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Bessel functions $I_{\nu }(x)$ and $K_{\nu }(x)$ of real order and complex argument. Comput. Phys. Comm. 24 (1), pp. 97–105.

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Double-precision Fortran, maximum accuracy 16S. For erratum see same journal 25 (1982), p. 207.

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ISSN 0010-4655, Document, Code

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2nd item.

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On zeros of the hypergeometric function. Serdica 7 (3), pp. 243–249.

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ISSN 0204-4140, MathReview (R. G. Buschman), ZentralBlatt

Referenced by:

§15.13.

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Numerical evaluation of Airy functions with complex arguments. J. Comput. Phys. 99 (1), pp. 106–114.

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ISSN 0021-9991, Document, MathReview, ZentralBlatt

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4th item, 1st item.

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Tables of Jacobian Elliptic Functions Whose Arguments are Rational Fractions of the Quarter Period. National Physical Laboratory Mathematical Tables, Vol. 7, Her Majesty’s Stationery Office, London.

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ISBN 00-791-1158-0, MathReview (John Todd), ZentralBlatt

Referenced by:

§22.20(vii), §22.21.

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22: Bibliography M

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Hypergeometric Functions.

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Unpublished Lecture Notes, University of London. An online version exists.

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FullText

Referenced by:

§35.7(ii), §35.8(iii).

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The dilogarithm function for complex argument. Proc. Roy. Soc. London Ser. A 459, pp. 2807–2819.

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ISSN 1364-5021, Document, MathReview (Wadim Zudilin), ZentralBlatt

Referenced by:

(25.12.1), (25.12.2), (25.12.3), (25.12.4), (25.12.5), (25.12.6), (25.12.7), (25.12.8), (25.12.9), §25.12(ii), §25.12(i), §25.12(i), §25.12(i), §25.12.

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Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

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ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(iii).

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Derivatives of the Hurwitz zeta function for rational arguments. J. Comput. Appl. Math. 100 (2), pp. 201–206.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

(25.11.21), (25.11.22), (25.11.23), §25.11, §25.11(vi), §25.18(i), (25.6.15).

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The dilogarithm function of a real argument. Math. Comp. 33 (146), pp. 778–787.

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

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2nd item, 4th item.

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23: Bibliography F

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Theory and Computation of Spheroidal Harmonics with General Arguments. Master’s Thesis, The University of Western Australia, Department of Physics.

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Contains Mathematica package for spheroidal wave functions of complex arguments with complex parameters.

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FullText

Referenced by:

§30.12, 1st item, 2nd item.

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Uniform asymptotic expansions for hypergeometric functions with large parameters IV. Anal. Appl. (Singap.) 12 (6), pp. 667–710.

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ISSN 0219-5305, Document, Link, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§15.12(iii), §15.12(iii).

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Expansions of hypergeometric functions in hypergeometric functions. Math. Comp. 15 (76), pp. 390–395.

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FullText, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§16.10.

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Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments. National Physical Laboratory Mathematical Tables, Vol. 4. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.

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MathReview (L. J. Slater), ZentralBlatt

Referenced by:

3rd item, 2nd item.

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Error bounds for the asymptotic expansion of the ratio of two gamma functions with complex argument. SIAM J. Math. Anal. 23 (2), pp. 505–511.

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ISSN 0036-1410, Document, FullText, MathReview (A. Reinfelds), ZentralBlatt

Referenced by:

§5.11(iii), §5.11(iii).

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24: Bibliography D

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Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.

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Document

Referenced by:

§13.28(iii).

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Bernoulli Numbers and Confluent Hypergeometric Functions. In Number Theory for the Millennium, I (Urbana, IL, 2000), pp. 343–363.

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ISBN 1-56881-126-8, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.16(iii).

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Bessel functions $J_n(z)$ and $Y_n(z)$ of integer order and complex argument. Comput. Phys. Comm. 78 (1-2), pp. 181–189.

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Double-precision Pascal, maximum accuracy 7D.

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ISSN 0010-4655, Document, Code, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

2nd item.

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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

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Notes:

(This reference has several typographical errors.)

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ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

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Conical functions of purely imaginary order and argument. Proc. Roy. Soc. Edinburgh Sect. A 143 (5), pp. 929–955.

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ISSN 0308-2105, Document, Link, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§14.20(ix), §14.20(ix).

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25: Bibliography

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Computation of the regular confluent hypergeometric function. The Mathematica Journal 5 (4), pp. 74–76.

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ISSN 1047-5974, FullText

Referenced by:

§13.32(iii).

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Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.

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ISSN 0373-1243, MathReview, ZentralBlatt

Referenced by:

§13.29(iii).

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A subroutine package for Bessel functions of a complex argument and nonnegative order. Technical Report Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.

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FullText

Referenced by:

1st item, B. Döring (1966).

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Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order. ACM Trans. Math. Software 12 (3), pp. 265–273.

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Notes:

Single and double precision, maximum accuracy 18S.

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ISSN 0098-3500, Document, Remark #1. Remark #2. GAMS (module 644; package TOMS), MathReview Entry, ZentralBlatt

Referenced by:

1st item, 1st item, 2nd item, 1st item.

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Spherical Bessel functions $j_n$ and $y_n$ of integer order and real argument. Comput. Phys. Comm. 14 (3-4), pp. 261–265.

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Notes:

Single-precision Fortran, maximum accuracy 10S.

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ISSN 0010-4655, Document, Code

Referenced by:

1st item.

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BibTeX

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