Zero-balanced G-function of Meijer and representations of generalized hypergeometric functions

15:00 07-11-2013
Colloquium in Mathematics and Computer Science
 
Dr. Dmitrii Karp, School of Economics and Management, Far Eastern Federal University, Vladivostok, Russia
 

7.11.13, 15:00 Science Building 8, Room 424

 
Abstract:

Meijer's G-function generalizes many elementary and special functions including hypergeometric functions and allows to give reasonable meaning to the symbol pFq when p > q +1 and the series defining the generalized hypergeometric function pFq diverges everywhere except for the origin.
 
Very recently, Meijer's G- function popped up naturally in the random matrix theory. It's various applications in statistics have been known for some decades. In the talk we discuss Meijer's G-function of the certain special type in the case when the difference of sums of upper and lower parameters is zero or negative integer.
 
In this situation, its behavior in the neighborhood of the regular singular point 1 seem to remain understudied. We find a representation of this function in this neighborhood and give applications to formulas for generalized hypergeometric functions of Gauss and Kummer type. In particular, we demonstrate the generalized Stieltjes and Laplace transform representations with measures containing an atom at 1.
 
A curious formula for a sum of products of the sine functions which revealed itself during the derivation of the main results will also be presented.
 
For further information:
Dr. David Garber, Department of Applied Mathematics, Faculty of Sciences,
Holon Institute of Technology
Tel/Fax: +972-3-5026737 | E-mail:
garber@hit.ac.il