q-Difference equations and iterated fractional q-integrals

Speaker:   曹健 教授 (杭州师范大学理学院)

Inviter:  陈绍示 （中国科学院数学机械化重点实验室）

Title:  q-Difference equations and iterated fractional q-integrals

Time & Venue:  202091 16:00-17:00

Abstract:

In this talk, we show how to prove identities and evaluate integrals by expanding functions in terms of products of the $q$-polynomials by homogeneous and $q$-partial difference equations, we also generalize some results of M.E.H. Ismail, Rui-Ming Zhang and Zhi-Guo Liu. In addition, we generalize multilinear and multiple generating functions for the $q$-polynomials as applications. Moreover, we deduce some recurring formulas for Ramanujan integrals, Askey--Roy integrals and Andrews--Askey integrals by the solutions of $q$-difference equations. At last, we generalize some iterated fractional q-integrals and build the relations of fractional q-integrals and q-Mittag-Leffler function.