The perturbed Bessel equation, I. A Duality Theorem

Details The perturbed Bessel equation, I. A Duality Theorem The perturbed Bessel equation, I. A Duality Theorem

Publishing date

2012-03-25

URL

arxiv.org/abs/1203.5550v1

Science

Mathematics

Field

Classical Analysis and ODEs

Type

Scientific paper

Abstract

The Euler-Gauss linear transformation formula for the hypergeometric function was extended by Goursat for the case of logarithmic singularities. By replacing the perturbed Bessel differential equation by a monodromic functional equation, and studying this equation separately from the differential equation by an appropriate Laplace-Borel technique, we associate with the latter equation another monodromic relation in the dual complex plane. This enables us to prove a duality theorem and to extend Goursat's formula to much larger classes of functions.

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