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11: Bibliography F

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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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External Links:

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

Referenced by:

§15.12(iii), §15.12(iii).

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Uniform asymptotic expansions of certain classes of Meijer $G$-functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.

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External Links:

Document, MathReview (C. M. Joshi), ZentralBlatt

Referenced by:

§16.22.

Encodings:

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Uniform asymptotic expansions of a class of Meijer $G$-functions for a large parameter. SIAM J. Math. Anal. 14 (6), pp. 1204–1253.

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External Links:

ISSN 0036-1410, Document, MathReview (Roop N. Kesarwani), ZentralBlatt

Referenced by:

§16.22.

Encodings:

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12: Preface

… ►Undoubtedly, the editors have overlooked some individuals who contributed, as is inevitable in a large long-lasting project. …

13: 16.22 Asymptotic Expansions

… ►Asymptotic expansions of $G_{p,q}^{m,n}(z;𝐚;𝐛)$ for large $z$ are given in Luke (1969a, §§5.7 and 5.10) and Luke (1975, §5.9). …

14: 12.11 Zeros

… ►When $a>-\frac{1}{2}$ the zeros are asymptotically given by $z_{a,s}$ and $\overline{z_{a,s}}$, where $s$ is a large positive integer and … ►For large negative values of $a$ the real zeros of $U(a,x)$, $U^{\prime }(a,x)$, $V(a,x)$, and $V^{\prime }(a,x)$ can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii). …

15: Bibliography W

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Mathematical Software for the P.C. and Work Stations – A Collection of Fortran 77 Programs. North-Holland Publishing Co., Amsterdam.

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Notes:

Translated from the 1989 Japanese original. With 1 IBM-PC floppy disk (5.25 inch) containing a large general purpose mathematical software collection written in Fortran, including some special function codes. Double precision.

External Links:

ISBN 0-444-82000-0, MathReview, ZentralBlatt

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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Hill’s equation with a large potential. SIAM J. Appl. Math. 45 (2), pp. 200–214.

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External Links:

ISSN 0036-1399, Document, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§29.7(ii).

Encodings:

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Wave functions for large arguments by the amplitude-phase method. Phys. Rev. 52, pp. 1123–1127.

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External Links:

Document, ZentralBlatt

Referenced by:

§33.5(ii).

Encodings:

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An asymptotic expansion of $W_{k,m}(z)$ with large variable and parameters. Math. Comp. 27 (122), pp. 429–436.

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External Links:

FullText, Document, MathReview (J. A. Donaldson), ZentralBlatt

Referenced by:

§13.19.

Encodings:

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16: Bibliography Z

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Computation of Special Functions. John Wiley & Sons Inc., New York.

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Notes:

Includes diskette containing a large collection of mathematical function software written in Fortran. Implementation in double precision. Maximum accuracy 16S.

External Links:

ISBN 0-471-11963-6, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

6th item, 3rd item, 1st item, 11st item, 7th item, 2nd item, 6th item, 3rd item, 2nd item, 5th item, 8th item, 4th item, 2nd item, §19.37(ii), §19.37(iii), §19.37(iii), §22.21, §24.19(i), §28.1, item (b), item (d), 8th item, 3rd item, 6th item, §5.22(ii), §5.22(iii), 2nd item, 2nd item, 4th item, 2nd item, 2nd item, §8.17(v), 4th item, 2nd item, 5th item, 3rd item, 3rd item, 3rd item, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

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17: 8.18 Asymptotic Expansions of $I_x(a,b)$

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Large $a$, Fixed $b$

… ►For asymptotic expansions for large values of $a$ and/or $b$ of the $x$-solution of the equation …

18: Bibliography N

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Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes. ACM Trans. Math. Software 18 (3), pp. 345–349.

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Notes:

Double-precision Fortran, minimum accuracy 9S, maximum accuracy 13S.

External Links:

ISSN 0098-3500, Document, GAMS (module 707; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

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Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes. J. Comput. Appl. Math. 39 (2), pp. 193–200.

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Notes:

Extended-precision Fortran evaluator, minimum accuracy 9S, maximum accuracy 13S.

External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§13.32(iii).

Encodings:

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Coulomb Functions for Large Values of the Parameter $\eta$ . Technical report Atomic Energy of Canada Limited, Chalk River, Ontario.

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Notes:

Rep. CRT-526

External Links:

MathReview (A. Erdélyi)

Referenced by:

§33.7.

Encodings:

BibTeX

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Notes:

A large general purpose mathematical software collection containing some special function codes. Implementation is in single precision.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

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19: 36.12 Uniform Approximation of Integrals

… ►where $k$ is a large real parameter and $𝐲=\{y_1,y_2,\mathrm{\dots }\}$ is a set of additional (nonasymptotic) parameters. …

20: 8.12 Uniform Asymptotic Expansions for Large Parameter

… ►Lastly, a uniform approximation for $\mathrm{\Gamma }(a,ax)$ for large $a$, with error bounds, can be found in Dunster (1996a). …