The Q-Gamma and Q-Beta Functions

Abstract

F. H. Jackson defined a q-analogue of the gamma function which extends the q-factorial [formula ommited]. This function is examined and analogues of many of the classical facts about the gamma function are obtained. These include an analogue of the Bohr-Mollerup theorem, an asymptotic formula for large x, the duplication formula, and two connections with sums that approximate beta function integrals. The behavior of this function as q changes is also considered. © 1978, Taylor & Francis Group, LLC. All rights reserved.