- Title
- Euler-Goursat-like formula via Laplace-Borel duality
- Creator
- Gurarii, V. P.; Gillam, David
- Date
- 2013
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/59454
- Identifier
- vital:5155
- Identifier
-
https://doi.org/10.1016/j.jmaa.2013.06.033
- Identifier
- ISSN:0022-247X
- Abstract
- 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. © 2013 Elsevier Ltd.; C1
- Relation
- Journal of Mathematical Analysis and Applications Vol. 408, no. 2 (2013), p. 655-668
- Rights
- Copyright Elsevier
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0906 Electrical and Electronic Engineering; Bessel differential equation; Error bounds; Euler linear transformation formula; Linear spaces of hypergeometric functions; Monodromic relation; Stokes phenomenon
- Full Text
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