About the Project

Euler-product representation


(0.002 seconds)

1—10 of 178 matching pages

1: 21.10 Methods of Computation
  • Belokolos et al. (1994, Chapter 5) and references therein. Here the Riemann surface is represented by the action of a Schottky group on a region of the complex plane. The same representation is used in Gianni et al. (1998).

  • 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 ber ν ( x 2 ) , bei ν ( x 2 ) , and their ν -derivatives. …
    4: 18.10 Integral Representations
    §18.10 Integral Representations
    5: 12.18 Methods of Computation
    These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions. …
    6: 16.7 Relations to Other Functions
    Further representations of special functions in terms of F q p functions are given in Luke (1969a, §§6.2–6.3), and an extensive list of F q q + 1 functions with rational numbers as parameters is given in Krupnikov and Kölbig (1997).
    7: 16.25 Methods of Computation
    Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations. …
    8: Wolter Groenevelt
    Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. …
    9: 13.27 Mathematical Applications
    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. …
    10: 14.32 Methods of Computation
    In particular, for small or moderate values of the parameters μ and ν 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. …
  • Quadrature (§3.5) of the integral representations given in §§14.12, 14.19(iii), 14.20(iv), and 14.25; see Segura and Gil (1999) and Gil et al. (2000).