$q$-analogs of sinc sums and integrals

Abstract

$q$-analogs of sum equals integral relations ${\sum }_{n\in \mathbb{Z}}f(n)={\int }_{-\infty }^{\infty }f(x)dx$ for sinc functions and binomial coefficients are studied. Such analogs are already known in the context of $q$-hypergeometric series. This paper deals with multibasic `fractional' generalizations that are not $q$-hypergeometric functions.

8 pages