Showing papers on "q-gamma function published in 2007"
TL;DR: In this article, Jackson defined a q-analogue of the gamma function which extends the q-factorial, and analogues of many of the classical facts about gamma function are obtained.
Abstract: F. H. Jackson defined q-analogue of the gamma function which extends the q-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 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
TL;DR: The results improve, complement, and generalize some known (nonsharp) estimates, and present several sharp inequalities for the classical gamma and q-gamma functions.