The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 7, 2023 at 2:00 pm (UTC+2)  in Room 478 of IMI.

A talk on:

New and little known properties of the Fox and Fox-Wright functions

 will be delivered by Dmitrii Karp, Holon Institute of Technology, Holon, Israel.

Everybody is invited.

Abstract.In the talk, I will introduce the functions H of Fox and W of Wright (its general case known as Fox-Wright function) and some motivation behind them. Then, I will discuss the extension of Gauss’ expansion and summation formulas for the hypergeometric function to the case of general Fox-Wright function and Norlund’s expansion for the Meijer’s G function to the case of Fox’s H function. I will further present positivity conditions for the so-called delta-neutral case of Fox’s H function making it a probability distribution (widely used in statistics), which rely on complete monotonicity of certain product ratios of Gamma functions. Moreover, I will exhibit a new integral equation for Fox’s H function and a conjecture regarding its zeros. Finally, some open problems will be presented.