Euler-Goursat-like formula via Laplace-Borel duality

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Gurarii, V. P.¹  Gillam, D. W. H.² 

[1] Swinburne Univ Technol, Hawthorn, Vic 3122, Australia

[2] Univ Ballarat, Sch Sci Informat Technol & Engn, Ballarat, Vic 3353, Australia

关键词: Euler linear transformation formula;    Monodromic relation;    Bessel differential equation;    Linear spaces of hypergeometric functions;    Stokes phenomenon;    Error bounds;   

DOI  :  10.1016/j.jmaa.2013.06.033

来源: Elsevier

【 摘 要 】

The Goursat formula for the hypergeometric function extends the Euler-Gauss relation to the case of logarithmic singularities. We study the monodromic functional equation associated with a perturbation of the Bessel differential equation by means of a variant of the Laplace-Borel technique: we introduce and study a related monodromic equation in the dual complex plane. This construction is a crucial element in our proof of a duality theorem that leads to an extension of the Euler-Gauss-Goursat formula for hypergeometric functions to a substantially larger class of functions. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free