Some properties and expansions associated with the q-digamma function

Abstract

This paper is devoted to derive some properties and expansions associated with the q-digamma function. The Newton series which is consisting of terms of forward difference operator, is established for the q-digamma function. The maltiplication formula of the q-gamma function is used to present some recurrence relations for the q-digamma function. The q-analogue of well-known results in the theory of the digamma function are investigated. One of the most important identities of q-beta integrals is used to introduce some integral representations of the q-digamma function.

Keywords: q-digamma function, q-gamma function, Newton series, q-maltiplication formula, q-beta integrals

Quaestiones Mathematicae 36(2013), 67–77