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11: Bibliography P

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Exponentially small expansions of the confluent hypergeometric functions. Appl. Math. Sci. (Ruse) 7 (133-136), pp. 6601–6609.

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ISSN 1312-885X, Document, MathReview Entry

Referenced by:

§13.7(iii), §13.7(iii).

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A numerical evaluator for the generalized hypergeometric series. Comput. Phys. Comm. 77 (2), pp. 249–254.

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Notes:

Extended-precision Fortran, maximum accuracy 12D.

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Document, Code, ZentralBlatt

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1st item.

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

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ISSN 0010-4655, Document, Code

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6th item.

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Chebyshev series approximations for the zeros of the Bessel functions. J. Comput. Phys. 53 (1), pp. 188–192.

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ISSN 0021-9991, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.76(ii).

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Integrals and Series: Special Functions, Vol. 2. Gordon & Breach Science Publishers, New York.

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Notes:

A second edition was published in 1988. Table errata: Math. Comp. v. 65 (1996), no. 215, pp. 1382–1383

External Links:

ISBN 2-88124-097-6, MathReview, ZentralBlatt

Referenced by:

§1.14(viii), §1.4(iv), §10.22(vi), §10.23(iv), §10.43(v), §10.43(vi), §10.44(iv), §10.60(iv), §10.71(iii), §12.12, §12.13(ii), §18.17(ix), §18.18(ix), §25.7, §25.8, §5.13, §6.14(iii), §6.15, §7.14(iii), §7.15, §8.14, §8.15.

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12: Bibliography C

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Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams. J. Comput. Appl. Math. 115 (1-2), pp. 93–99.

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ISSN 0377-0427, Document, MathReview (Lorenzo L. Salcedo), ZentralBlatt

Referenced by:

§16.24(ii).

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Expansions in terms of parabolic cylinder functions. Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.

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MathReview (I. I. Hirschman, Jr.), ZentralBlatt

Referenced by:

§12.16.

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Chebyshev expansions for the Bessel function $J_n(z)$ in the complex plane. Math. Comp. 40 (161), pp. 343–366.

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ISSN 0025-5718, FullText, MathReview (C. W. Clenshaw), ZentralBlatt

Referenced by:

§10.76(ii).

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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

Referenced by:

§13.29(v), §15.19(v).

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A sequence of series for the Lambert $W$ function. In Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), pp. 197–204.

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Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(4.13.4_1), (4.13.4_2), (4.13.5_2), §4.13.

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13: Bibliography

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Hypergeometric Functions and Elliptic Integrals. In Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa (Eds.), pp. 48–85.

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MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§19.9(i).

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On basic hypergeometric series, mock theta functions, and partitions. II. Quart. J. Math. Oxford Ser. (2) 17, pp. 132–143.

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Document, MathReview (B. R. Bhonsle), ZentralBlatt

Referenced by:

§17.6(ii).

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Special value of the hypergeometric function ${}_3{}^{}F_2^{}$ and connection formulae among asymptotic expansions. J. Indian Math. Soc. (N.S.) 51, pp. 161–221.

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ISSN 0019-5839, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§16.4(iii).

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Modular Functions and Dirichlet Series in Number Theory. 2nd edition, Graduate Texts in Mathematics, Vol. 41, Springer-Verlag, New York.

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ISBN 0-387-97127-0, MathReview, ZentralBlatt

Referenced by:

§17.2(i), §23.10(iv), §23.15(i), §23.17(ii), §23.18, §23.18, §23.19, §23.20(i), §23.20(v), Ch.23, §27.14(iii), §27.14(iv), §27.14(vi), §27.7, Ch.27.

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Orthogonal Polynomials and Special Functions. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 21, Society for Industrial and Applied Mathematics, Philadelphia, PA.

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External Links:

ISBN 0-89871-018-9, MathReview (G. Gasper), ZentralBlatt

Referenced by:

§18.10(ii), §18.18(vii), Profile Richard A. Askey.

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14: Bibliography B

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Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.

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Document, ZentralBlatt

Referenced by:

§16.12.

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A short table of the functions ${\mathrm{Ki}}_n(x)$, from $n=1$ to $n=16$ . Phil. Mag. Series 7 20, pp. 343–347.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.43(iii), 2nd item.

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

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Expansions of Appell’s double hypergeometric functions. Quart. J. Math., Oxford Ser. 11, pp. 249–270.

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External Links:

Document, MathReview (G. Szegő), ZentralBlatt

Referenced by:

§15.16, (16.15.4), §16.15, §16.16(i).

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Expansions of Appell’s double hypergeometric functions. II. Quart. J. Math., Oxford Ser. 12, pp. 112–128.

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Document, MathReview (G. Szegő), ZentralBlatt

Referenced by:

§16.16(i).

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15: 2.11 Remainder Terms; Stokes Phenomenon

… ►Secondly, the asymptotic series represents an infinite class of functions, and the remainder depends on which member we have in mind. … ►These answers are linked to the terms involving the complementary error function in the more powerful expansions typified by the combination of (2.11.10) and (2.11.15). … ►For illustration, we give re-expansions of the remainder terms in the expansions (2.7.8) arising in differential-equation theory. … ►In this way we arrive at hyperasymptotic expansions. … ►The transformations in §3.9 for summing slowly convergent series can also be very effective when applied to divergent asymptotic series. …

16: Bibliography W

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Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules. Ann. Inst. Statist. Math. 45 (3), pp. 467–475.

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ISSN 0020-3157, Document, MathReview (N. K. Thakare), ZentralBlatt

Referenced by:

§35.9.

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Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations. Computers in Physics 10 (5), pp. 496–503.

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Document

Referenced by:

§2.11(vi), §2.11(vi).

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Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions. In Algorithms for Approximation, A. Iske and J. Levesley (Eds.), pp. 331–348.

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External Links:

ISBN 3-540-33283-9, Document, MathReview Entry, ZentralBlatt

Referenced by:

§2.10(i).

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Some transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 26 (2), pp. 257–272.

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Document, ZentralBlatt

Referenced by:

§16.6.

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The asymptotic expansion of the generalized hypergeometric function. Proc. London Math. Soc. (2) 46, pp. 389–408.

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ISSN 0024-6115, Document, MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§16.11(ii).

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17: 8.17 Incomplete Beta Functions

§8.17 Incomplete Beta Functions

… ►where, as in §5.12, $\mathrm{B}(a,b)$ denotes the beta function: … ►

§8.17(ii) Hypergeometric Representations

… ►For the hypergeometric function $F(a,b;c;z)$ see §15.2(i). … ►For sums of infinite series whose terms involve the incomplete beta function see Hansen (1975, §62). …

18: Bibliography G

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Contiguous relations and summation and transformation formulae for basic hypergeometric series. J. Difference Equ. Appl. 19 (12), pp. 2029–2042.

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ISSN 1023-6198, Document, FullText, MathReview (Thomas Britz), ZentralBlatt

Referenced by:

§17.7(iii).

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Basic Hypergeometric Series. Encyclopedia of Mathematics and its Applications, Vol. 35, Cambridge University Press, Cambridge.

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Notes:

A revised and updated edition, with three new chapters, was published in 2004 by Cambridge University Press (Encyclopedia of Mathematics and its Applications, vol. 96).

External Links:

ISBN 0-521-35049-2, MathReview (Shaun Cooper), ZentralBlatt

Referenced by:

(17.9.3), Erratum (V1.0.23) for Equation (17.9.3).

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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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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

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

Referenced by:

3rd item, §10.77(ix).

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Multilateral summation theorems for ordinary and basic hypergeometric series in $\mathrm{U}(n)$ . SIAM J. Math. Anal. 18 (6), pp. 1576–1596.

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ISSN 0036-1410, Document, MathReview, ZentralBlatt

Referenced by:

§17.15.

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19: Bibliography L

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New method to obtain small parameter power series expansions of Mathieu radial and angular functions. Math. Comp. 78 (265), pp. 255–274.

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ISSN 0025-5718, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§28.24, §28.24.

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New series expansions for the confluent hypergeometric function $M(a,b,z)$ . Appl. Math. Comput. 235, pp. 26–31.

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ISSN 0096-3003, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§13.11, §13.11.

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New series expansions of the Gauss hypergeometric function. Adv. Comput. Math. 39 (2), pp. 349–365.

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ISSN 1019-7168, Document, FullText, MathReview (Jochen Denzler), ZentralBlatt

Referenced by:

§15.19(i), §15.19(i).

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Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray. Math. Comp. 17 (84), pp. 395–404.

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External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

2nd item.

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Expansion of the confluent hypergeometric function in series of Bessel functions. Math. Tables Aids Comput. 13 (68), pp. 261–271.

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External Links:

FullText, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§13.24(ii).

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