The perturbed Bessel equation, I. A Duality Theorem
Classical Analysis and ODEs
2015-10-01 v1 Functional Analysis
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.
Cite
@article{arxiv.1203.5550,
title = {The perturbed Bessel equation, I. A Duality Theorem},
author = {V. P. Gurarii and D. W. H. Gillam},
journal= {arXiv preprint arXiv:1203.5550},
year = {2015}
}