# The perturbed Bessel equation and Duality Theorem

Mon, 16/04/2012 - 15:05

Speaker:

, Swinburne University of Technology, Hawthorn, Australia Prof. V.P. Gurarii

Seminar:

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.

- Last modified: 29/03/2012