# Euler-product representation

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## 1—10 of 178 matching pages

##### 1: 21.10 Methods of Computation

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Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.

Deconinck and van Hoeij (2001). Here a plane algebraic curve representation of the Riemann surface is used.

##### 2: 26.19 Mathematical Applications

###### §26.19 Mathematical Applications

… ►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). …##### 3: 10.64 Integral Representations

###### §10.64 Integral Representations

… ►See Apelblat (1991) for these results, and also for similar representations for ${\mathrm{ber}}_{\nu}\left(x\sqrt{2}\right)$, ${\mathrm{bei}}_{\nu}\left(x\sqrt{2}\right)$, and their $\nu $-derivatives. …##### 4: 18.10 Integral Representations

##### 5: 12.18 Methods of Computation

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►These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions.
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##### 6: 16.7 Relations to Other Functions

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►Further representations of special functions in terms of ${}_{p}{}^{}F_{q}^{}$ functions are given in Luke (1969a, §§6.2–6.3), and an extensive list of ${}_{q+1}{}^{}F_{q}^{}$ functions with rational numbers as parameters is given in Krupnikov and Kölbig (1997).

##### 7: 16.25 Methods of Computation

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►Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations.
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##### 8: Wolter Groenevelt

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►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems.
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##### 9: 13.27 Mathematical Applications

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►Confluent hypergeometric functions are connected with representations of the group of third-order triangular matrices.
…Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function.
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##### 10: 14.32 Methods of Computation

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►In particular, for small or moderate values of the parameters $\mu $ and $\nu $ the power-series expansions of the various hypergeometric function representations given in §§14.3(i)–14.3(iii), 14.19(ii), and 14.20(i) can be selected in such a way that convergence is stable, and reasonably rapid, especially when the argument of the functions is real.
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