Completely monotonic functions related to the q-gamma and the q-trigamma functions

DOI10.1142/S0219530514500195zbMath1312.33046MaRDI QIDQ5248153

Ahmed Salem

Publication date: 27 April 2015

Published in: Analysis and Applications (Search for Journal in Brave)

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)

Related Items (14)

Bose–Einstein condensation of two-dimensional spin-1 Cooper pairs in a uniform magnetic field ⋮ Monotonic functions related to the \(q\)-gamma function ⋮ Sharp bounds for the \(q\)-gamma function in terms of the Lambert \(W\) function ⋮ Sharp lower and upper bounds for the q-gamma function ⋮ Exact analytical study of ideal Bose atoms in a one-dimensional harmonic trap ⋮ Exact spatial density of ideal Bose atoms in a one-dimensional harmonic trap ⋮ Exact thermodynamic theory of ideal Bose atoms in a two-dimensional isotropic harmonic trap ⋮ Two-step condensation of interacting bosons in three-dimensional isotropic harmonic traps ⋮ Completely monotonic functions related to the gamma and the \(q\)-gamma functions ⋮ Monotonicity properties of \(q\)-digamma and \(q\)-trigamma functions ⋮ Exact spatial density of ideal Bose atoms in a two-dimensional isotropic harmonic trap ⋮ 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 ⋮ Exact magnetic properties of two-dimensional spin-1 Cooper pairs

Cites Work

• Unnamed Item
• Two classes of bounds for \(q\)-gamma and \(q\)-digamma functions in terms of \(q\)-zeta functions
• A completely monotonic function involving \(q\)-gamma and \(q\)-digamma functions
• The q-analogue of Stirling's formula
• Inequalities for the gamma and \(q\)-gamma functions
• Completely monotonic functions associated with the gamma function and its q-analogues
• Convexity and \(q\)-gamma function
• Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function
• An infinite class of completely monotonic functions involving the \(q\)-gamma function
• Some properties of functions related to the gamma, psi and tetragamma functions
• Some properties and expansions associated with theq-digamma function
• Completely monotonic functions involving the gamma and $q$-gamma functions

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