Theq-Gamma andq-Beta Functions#x2020;

摘要

F. H. Jackson definedq-analogue of the gamma function which extends theq-factorial. 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 largex, the duplication formula, and two connections with sums that approximate beta function integrals. The behavior of this function asqchanges is also considered