\(q\)-extensions of some estimates associated with the digamma function

DOI10.1016/j.jat.2013.06.002zbMath1290.33017OpenAlexW2032163287MaRDI QIDQ390622

Necdet Batir

Publication date: 8 January 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2013.06.002

zbMATH Keywords

estimations\(q\)-digamma function

Mathematics Subject Classification ID

(q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (12)

Logarithmically completely monotonic functions related to the \(q\)-gamma function and its applications ⋮ Complete characterizations of the gamma function ⋮ Monotonic functions related to the \(q\)-gamma function ⋮ Sharp bounds for the \(q\)-gamma function in terms of the Lambert \(W\) function ⋮ Unnamed Item ⋮ Sharp lower and upper bounds for the q-gamma function ⋮ Completely monotonic functions related to the gamma and the \(q\)-gamma functions ⋮ Inequalities for \(q\)-gamma function ratios ⋮ Monotonicity properties of \(q\)-digamma and \(q\)-trigamma functions ⋮ Complete Monotonicity property for two functions related to the q-digamma function ⋮ Sharp bounds for a ratio of the \(q\)-gamma function in terms of the \(q\)-digamma function ⋮ Functional inequalities for the \(q\)-digamma function

Cites Work

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• A completely monotonic function involving \(q\)-gamma and \(q\)-digamma functions
• Some monotonicity properties of gamma and \(q\)-gamma functions
• On some properties of digamma and polygamma functions
• Inequalities for the gamma and \(q\)-gamma functions
• Inequalities for the gamma function
• Completely monotonic functions associated with the gamma function and its q-analogues
• The \(q\)-gamma function for \(q>1\)
• Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function
• Completely monotonic functions involving the gamma and $q$-gamma functions
• Theq-Gamma andq-Beta Functions†
• Sharp inequalities for the digamma and polygamma functions
• The best bounds in Gautschi's inequality
• Inequalities and monotonicity properties for gamma and q-gamma functions

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