Publication Cover
Applicable Analysis
An International Journal
Volume 8, 1978 - Issue 2
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Original Articles

The q-Gamma and q-Beta FunctionsFootnote

Pages 125-141 | Received 16 Sep 1977, Published online: 10 May 2007
 

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

†Dedicated to Professor A. Erdeélyi in appreciation of his mathematical work and scholarship.

‡Supported in part by N.S.F. grant MCS75-06687 mod 4.

†Dedicated to Professor A. Erdeélyi in appreciation of his mathematical work and scholarship.

‡Supported in part by N.S.F. grant MCS75-06687 mod 4.

Notes

†Dedicated to Professor A. Erdeélyi in appreciation of his mathematical work and scholarship.

‡Supported in part by N.S.F. grant MCS75-06687 mod 4.

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