The perturbed Bessel equation and Duality Theorem
Seminar
Speaker
, Swinburne University of Technology, Hawthorn, Australia Prof. V.P. Gurarii
Date
16/04/2012 - 15:05Add to Calendar
2012-04-16 15:05:00
2012-04-16 15:05:00
The perturbed Bessel equation and Duality Theorem
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.
אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
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 Updated Date : 29/03/2012
