Euler-Goursat-like formula via Laplace-Borel duality

[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.

[发布日期] 2013-12-15

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