relations%20to%20confluent%20hypergeometric%20functions%20of%20matrix%20argument

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1: Software Index

… ►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … ►In the list below we identify four main sources of software for computing special functions. … ►

These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.

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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

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A cross index of mathematical software in use at NIST.

2: Bibliography

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

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External Links:

ISSN 1047-5974, FullText

Referenced by:

§13.32(iii).

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On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.

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External Links:

ISSN 0024-1318, MathReview (James M. Horner)

Referenced by:

§13.9(i).

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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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Dirichlet series related to the Riemann zeta function. J. Number Theory 19 (1), pp. 85–102.

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ISSN 0022-314X, Document, MathReview (Kai Man Tsang), ZentralBlatt

Referenced by:

(25.16.10), (25.16.11), (25.16.12), (25.16.14), (25.16.15), (25.16.5), (25.16.6), (25.16.7), (25.16.8), (25.16.9), §25.16(ii), §25.16(ii), §25.16.

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Integral equations and relations for Lamé functions. Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.

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Document, MathReview (I. Marx), ZentralBlatt

Referenced by:

§29.8.

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3: Bibliography M

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Quadratic relations for confluent hypergeometric functions. Tohoku Math. J. (2) 52 (4), pp. 489–513.

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ISSN 0040-8735, Document, MathReview (Takeshi Sasaki), ZentralBlatt

Referenced by:

§13.12.

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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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Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions. Comput. Phys. Comm. 178 (7), pp. 535–551.

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

Referenced by:

§15.19(i), §15.19(i).

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A new symmetry related to $\mathrm{𝑆𝑈}(n)$ for classical basic hypergeometric series. Adv. in Math. 57 (1), pp. 71–90.

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ISSN 0001-8708, Document, MathReview (George E. Andrews), ZentralBlatt

Referenced by:

§17.15.

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A connection formula for the $q$-confluent hypergeometric function. SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 050, 13.

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ISSN 1815-0659, Document, MathReview (Jeremy Lovejoy), ZentralBlatt

Referenced by:

§17.6(ii), §17.6(ii).

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4: Bibliography G

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New inequalities for the zeros of confluent hypergeometric functions. In Asymptotic and computational analysis (Winnipeg, MB, 1989), pp. 175–192.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§13.9(i), §13.9(ii).

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Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38 (1), pp. 77–81.

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External Links:

MathReview (H. O. Pollak), ZentralBlatt

Referenced by:

§5.6(i), §6.8, §7.8, §8.10.

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Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions. J. Comput. Appl. Math. 139 (1), pp. 173–187.

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ISSN 0377-0427, Document, MathReview (Hasan Taşeli), ZentralBlatt

Referenced by:

§13.29(iii), §15.19(iii).

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Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions. Trans. Amer. Math. Soc. 301 (2), pp. 781–811.

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ISSN 0002-9947, FullText, MathReview (Wayne J. Holman, III), ZentralBlatt

Referenced by:

§35.8(i), §35.8(ii), §35.8(iv), Ch.35.

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Hypergeometric functions on complex matrix space. Bull. Amer. Math. Soc. (N.S.) 24 (2), pp. 349–355.

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ISSN 0273-0979, Document, MathReview, ZentralBlatt

Referenced by:

§35.7(iii), §35.8(i), §35.8(ii), §35.8(iii), §35.8(iv).

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