Whipple%20formula

SearchAdvancedHelp

(0.002 seconds)

1—10 of 307 matching pages

1: 14.19 Toroidal (or Ring) Functions

… ►

§14.19(v) Whipple’s Formula for Toroidal Functions

…

2: Bibliography W

… ►

Reduction formulae for products of theta functions. J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.

ⓘ

External Links:

Document

Referenced by:

(20.7.34), §20.7(ix).

Encodings:

BibTeX

… ►

Extension of a quadratic transformation due to Whipple with an application. Adv. Difference Equ., pp. 2013:157, 8.

ⓘ

External Links:

ISSN 1687-1847, Document, FullText, MathReview (Daniele Ritelli), ZentralBlatt

Referenced by:

§16.6, §16.6.

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§16.6.

Encodings:

BibTeX

… ►

Recursion formulae for hypergeometric functions. Math. Comp. 22 (102), pp. 363–373.

ⓘ

External Links:

FullText, Document, MathReview (S. D. Bajpai), ZentralBlatt

Referenced by:

§16.3(ii).

Encodings:

BibTeX

… ►

Quadrature formulas for oscillatory integral transforms. Numer. Math. 39 (3), pp. 351–360.

ⓘ

External Links:

ISSN 0029-599X, Document, MathReview (A.J. Rodrigues), ZentralBlatt

Referenced by:

§10.74(vii), §3.5(vii).

Encodings:

BibTeX

…

3: 14.9 Connection Formulas

§14.9 Connection Formulas

►

§14.9(i) Connections Between ${𝖯}_{\nu }^{\pm \mu }\left(x\right)$, ${𝖯}_{-\nu -1}^{\pm \mu }\left(x\right)$, ${𝖰}_{\nu }^{\pm \mu }\left(x\right)$, ${𝖰}_{-\nu -1}^{\mu }\left(x\right)$

… ►

§14.9(ii) Connections Between ${𝖯}_{\nu }^{\pm \mu }\left(\pm x\right)$, ${𝖰}_{\nu }^{-\mu }\left(\pm x\right)$, ${𝖰}_{\nu }^{\mu }\left(x\right)$

… ►

§14.9(iii) Connections Between $P_{\nu }^{\pm \mu }\left(x\right)$, $P_{-\nu -1}^{\pm \mu }\left(x\right)$, ${𝑸}_{\nu }^{\pm \mu }\left(x\right)$, ${𝑸}_{-\nu -1}^{\mu }\left(x\right)$

… ►

§14.9(iv) Whipple’s Formula

…

4: 16.4 Argument Unity

… ►

Whipple’s Sum

… ►Balanced ${}_4{}^{}F_3^{}\left(1\right)$ series have transformation formulas and three-term relations. … ►A different type of transformation is that of Whipple: … ►See Bailey (1964, §§4.3(7) and 7.6(1)) for the transformation formulas and Wilson (1978) for contiguous relations. …

5: Gergő Nemes

… ►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions. …

6: Wolter Groenevelt

… ►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials. …

7: Bibliography M

… ►

Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

ⓘ

Notes:

Includes Fortran code, maximum accuracy 20S.

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

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

Referenced by:

§10.74(iii).

Encodings:

BibTeX

… ►

A $q$-analog of a Whipple’s transformation for hypergeometric series in $U(n)$ . Adv. Math. 108 (1), pp. 1–76.

ⓘ

External Links:

ISSN 0001-8708, Document, MathReview, ZentralBlatt

Referenced by:

§17.15.

Encodings:

BibTeX

… ►

The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

ⓘ

External Links:

ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.27(v).

Encodings:

BibTeX

►

The $q$-analogue of Stirling’s formula. Rocky Mountain J. Math. 14 (2), pp. 403–413.

ⓘ

External Links:

ISSN 0035-7596, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§5.18(ii).

Encodings:

BibTeX

…

8: 17.9 Further Transformations of ${}_{r+1}{}^{}\varphi _r^{}$ Functions

… ►

Watson’s $q$-Analog of Whipple’s Theorem

… ►

Gasper’s $q$-Analog of Clausen’s Formula (16.12.2)

…

9: 20 Theta Functions

Chapter 20 Theta Functions

…

10: Foreword

… ►In 1964 the National Institute of Standards and Technology published the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz and Irene A. … ►November 20, 2009 …