Q extension of Wielandt's Theorem

Abstract

It is well known that the q-Gamma function cannot be characterised by its functional equation o q ( z + 1) =/((1 m q z )(1 m q )) o q ( z ) and the condition o q (1) = 1. In 1980 Richard Askey showed in [1] that the additional assumption of logarithmic convexity yields the uniqueness of o q ( x ) for real x > 0. The goal of this note is to establish a q-extension of Wielandt's theorem which gives a characterization of o q ( z ) for all $ z\\in \\{z\\in{\\shadC}:{\\rm Re}(z)\\gt 0\\} $ .