Two-sided inequality involving the \(q\)-gamma function

DOI10.1007/s40819-017-0476-4zbMath1380.33009OpenAlexW2777339970MaRDI QIDQ1688801

Faris Alzahrani, Ahmed Salem

Publication date: 11 January 2018

Published in: International Journal of Applied and Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40819-017-0476-4

zbMATH Keywords

inequalities\(q\)-gamma functioncompletely monotonic function\(q\)-polygamma functions

Mathematics Subject Classification ID

Monotonic functions, generalizations (26A48) (q)-gamma functions, (q)-beta functions and integrals (33D05) Inequalities involving other types of functions (26D07)

Cites Work

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• Two classes of bounds for \(q\)-gamma and \(q\)-digamma functions in terms of \(q\)-zeta functions
• The q-analogue of Stirling's formula
• A remark on a class of double inequalities of Batir
• The \(q\)-gamma function for \(q>1\)
• A note on \(q\)-analogues of the Dirichlet series and \(q\)-Bernoulli numbers
• Asymptotic expansions for \(q\)-gamma, \(q\)-exponential, and \(q\)-Bessel functions
• Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function
• A certain class of approximations for the \(q\)-digamma function
• On some properties of the gamma function
• Some properties and expansions associated with theq-digamma function
• Theq-Gamma andq-Beta Functions†
• Improvements of bounds for the q-gamma and the $q$-polygamma functions

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