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31: 8.20 Asymptotic Expansions of $E_p\left(z\right)$

… ►For further information, including extensions to complex values of $x$ and $p$, see Temme (1994b, §4) and Dunster (1996b, 1997).

32: 17.13 Integrals

… ►Askey (1980) conjectured extensions of the foregoing integrals that are closely related to Macdonald (1982). …

33: 2.5 Mellin Transform Methods

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§2.5(ii) Extensions

… ►Following Handelsman and Lew (1970, 1971) we now give an extension of this method in which none of these conditions is required. … ►Furthermore, each $G_{jk}(z)$ has an analytic or meromorphic extension to a half-plane containing $D_{jk}$. … ►See also Brüning (1984) for a different approach. …

34: 2.3 Integrals of a Real Variable

… ►For an extension with more general $t$-powers see Bleistein and Handelsman (1975, §4.1). … ►Another extension is to more general factors than the exponential function. … ►For extensions to oscillatory integrals with more general $t$-powers and logarithmic singularities see Wong and Lin (1978) and Sidi (2010). …

35: 4.40 Integrals

… ►Extensive compendia of indefinite and definite integrals of hyperbolic functions include Apelblat (1983, pp. 96–109), Bierens de Haan (1939), Gröbner and Hofreiter (1949, pp. 139–160), Gröbner and Hofreiter (1950, pp. 160–167), Gradshteyn and Ryzhik (2000, Chapters 2–4), and Prudnikov et al. (1986a, §§1.4, 1.8, 2.4, 2.8).

36: 13.21 Uniform Asymptotic Approximations for Large $\kappa$

… ►For (13.21.6), (13.21.7), and extensions to asymptotic expansions and error bounds, see Olver (1997b, Chapter 12, Exs. 12.4.5, 12.4.6). For extensions to complex values of $x$ see López (1999). … ►This reference also includes error bounds and extensions to asymptotic expansions and complex values of $x$. … ►This reference also includes error bounds and extensions to asymptotic expansions and complex values of $x$. …

37: 17.14 Constant Term Identities

… ►Macdonald (1982) includes extensive conjectures on generalizations of (17.14.1) to root systems. …

38: 20.11 Generalizations and Analogs

… ►Each provides an extension of Jacobi’s inversion problem. …

39: 36.7 Zeros

… ►For a more extensive asymptotic analysis and further tabulations, see Kaminski and Paris (1999). …

40: Bibliography

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An integral of products of ultraspherical functions and a $q$-extension. J. London Math. Soc. (2) 33 (1), pp. 133–148.

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External Links:

ISSN 0024-6107, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§10.22(iv), §14.30(ii).

Encodings:

BibTeX

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Some basic hypergeometric extensions of integrals of Selberg and Andrews. SIAM J. Math. Anal. 11 (6), pp. 938–951.

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External Links:

ISSN 0036-1410, Document, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§17.13, §17.13.

Encodings:

BibTeX

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