Completely monotonic gamma ratio and infinitely divisible H-function of Fox

Seminar
Speaker
Prof. Dmitry Karp, Institute of Applied Mathematics, Far Eastern Branch of Russian Academy of Sciences, Russia
Date
12/11/2018 - 15:25 - 14:00Add to Calendar 2018-11-12 14:00:00 2018-11-12 15:25:00 Completely monotonic gamma ratio and infinitely divisible H-function of Fox We investigate conditions for the logarithmic complete monotonicity of a quotient of two products of gamma functions, where the argument of each gamma function has a different scaling factor. We give necessary and sufficient conditions in terms of non-negativity of some elementary functions and some more practical sufficient conditions in terms of parameters. Further, we study the representing measure in Bernstein’s theorem for both equal and non-equal scaling factors. This leads to conditions on the parameters under which Meijer’s G-function or Fox’s H-function represents an infinitely divisible probability distribution on the positive half-line. 2nd floor Colloquium Room, Building 216 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
2nd floor Colloquium Room, Building 216
Abstract

We investigate conditions for the logarithmic complete
monotonicity of a quotient of two products of gamma functions, where
the argument of each gamma function has a different scaling factor. We
give necessary and sufficient conditions in terms of non-negativity of
some elementary functions and some more practical sufficient
conditions in terms of parameters. Further, we study the representing
measure in Bernstein’s theorem for both equal and non-equal scaling
factors. This leads to conditions on the parameters under which Meijer’s
G-function or Fox’s H-function represents an infinitely divisible
probability distribution on the positive half-line.

תאריך עדכון אחרון : 10/11/2018