Sharp bounds for the \(q\)-gamma function in terms of the Lambert \(W\) function
From MaRDI portal
Publication:2422141
DOI10.1007/s11139-018-0008-9zbMath1431.33018OpenAlexW2803550183WikidataQ129813633 ScholiaQ129813633MaRDI QIDQ2422141
Publication date: 18 June 2019
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-018-0008-9
inequalities\(q\)-gamma functioncompletely monotonic functionLambert \(W\) function\(q\)-polygamma functions
Monotonic functions, generalizations (26A48) (q)-gamma functions, (q)-beta functions and integrals (33D05) Inequalities involving other types of functions (26D07)
Related Items (6)
A harmonic mean inequality for the \(q\)-gamma function ⋮ Sharp lower and upper bounds for the q-gamma function ⋮ 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 ⋮ Best bounds for the Lambert W functions
Cites Work
- Unnamed Item
- \(q\)-extensions of some estimates associated with the digamma function
- A completely monotonic function involving \(q\)-gamma and \(q\)-digamma functions
- Complete monotonicity of functions involving the \(q\)-trigamma and \(q\)-tetragamma functions
- Completely monotonic functions related to the gamma and the \(q\)-gamma functions
- Some completely monotonic functions associated with the \(q\)-gamma and the \(q\)-polygamma functions
- The q-analogue of Stirling's formula
- An ultimate extremely accurate formula for approximation of the factorial function
- The \(q\)-gamma function for \(q>1\)
- On the Lambert \(w\) function
- Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function
- Monotonicity properties of \(q\)-digamma and \(q\)-trigamma functions
- An infinite class of completely monotonic functions involving the \(q\)-gamma function
- A certain class of approximations for the \(q\)-digamma function
- Monotonic functions related to the \(q\)-gamma function
- Some classes of completely monotonic functions related to q-gamma and q-digamma functions
- Some properties and expansions associated with theq-digamma 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
- Theq-Gamma andq-Beta Functions†
- Inequalities and monotonicity properties for gamma and q-gamma functions
- Complete monotonicity properties of functions involving q-gamma and q-digamma functions
- Completely monotonic functions related to the q-gamma and the q-trigamma functions
- Improvements of bounds for the q-gamma and the $q$-polygamma functions
This page was built for publication: Sharp bounds for the \(q\)-gamma function in terms of the Lambert \(W\) function
