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The q -Gamma and q -Beta Functions†

1978; Taylor & Francis; Volume: 8; Issue: 2 Linguagem: Inglês

10.1080/00036817808839221

1563-504X

Richard Askey,

Advanced Statistical Methods and Models

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.