Finite Group Actions and Asymptotic Expansion of 1995 5 citations ? 4 self

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  • Author:  by Thomas M?ller  Thomas M  Fakultat Fur Mathematik  Thomas M Uller  

  • Abstract:  . We establish an asymptotic expansion for the number jHom(G; S n )j of actions of a finite group G on an n-set in terms of the order jGj = m and the number s G (d) of subgroups of index d in G for djm: This expansion and related results on the enumeration of finite group actions follow from more general results concerning the asymptotic behaviour of the coefficients of entire functions of finite genus with finitely many zeros. As another application of these analytic considerations we establish an asymptotic property of the Hermite polynomials, leading to the explicit determination of the coefficients C (ff; z) in Perron's asymptotic expansion for Laguerre polynomials in the cases ff = \Sigma1=2: Contents 1. Introduction 2. Asymptotic expansion of e P (z) e P (z) e P (z) : Hayman's method 3. Asymptotic expansion of e P (z) e P (z) e P (z) : The method of Harris and Schoenfeld 3.1 The result 3.2 The method of Harris and Schoenfeld 3.3 HS-admissibility of exp \Gamma P (...

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