Completely monotonic functions involving the gamma and $q$-gamma functions
From MaRDI portal
Publication:3372092
DOI10.1090/S0002-9939-05-08050-0zbMath1085.33001OpenAlexW1761810493MaRDI QIDQ3372092
Arcadii Z. Grinshpan, Mourad E. H. Ismail
Publication date: 17 February 2006
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-05-08050-0
gamma functioninequalities\(q\)-gamma functioncompletely monotonic functionsinfinitely divisible probability distributions
Gamma, beta and polygamma functions (33B15) Monotonic functions, generalizations (26A48) (q)-gamma functions, (q)-beta functions and integrals (33D05)
Related Items (54)
Representations and inequalities for generalized hypergeometric functions ⋮ A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality ⋮ Logarithmically completely monotonic functions concerning gamma and digamma functions ⋮ Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions ⋮ Complete monotonicity of some functions involving polygamma functions ⋮ Inequalities for the gamma and \(q\)-gamma functions ⋮ Positivity and Hankel transforms ⋮ Ratios of entire functions and generalized Stieltjes functions ⋮ Complete monotonicity involving some ratios of gamma functions ⋮ \(q\)-extensions of some estimates associated with the digamma function ⋮ Some exact constants for the approximation of the quantity in the Wallis' formula ⋮ Monotonicity, convexity, and inequalities for functions involving gamma function ⋮ Inequalities for gamma and q-gamma functions of complex arguments ⋮ An integral recursive inequality and applications ⋮ Functional definitions for \(q\)-analogues of Eulerian functions and applications ⋮ On some properties of the gamma function ⋮ \(q\)-Bessel positive definite and \(D _{q }\)-completely monotonic functions ⋮ On complete monotonicity of certain special functions ⋮ INEQUALITIES AND COMPLETE MONOTONICITY FOR THE GAMMA AND RELATED FUNCTIONS ⋮ A completely monotonic function involving \(q\)-gamma and \(q\)-digamma functions ⋮ Complete monotonicity of a function involving the ratio of gamma functions and applications ⋮ Bounds for the ratio of two gamma functions -- from Wendel's and related inequalities to logarithmically completely monotonic functions ⋮ From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions ⋮ Monotonicity, concavity, and inequalities related to the generalized digamma function ⋮ Weighted inequalities and negative binomials ⋮ Sharp lower and upper bounds for the q-gamma function ⋮ Weighted integral and integro-differential inequalities ⋮ Complete monotonicity of functions involving the \(q\)-trigamma and \(q\)-tetragamma functions ⋮ A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality ⋮ An extension and a refinement of van der Corput's inequality ⋮ Accurate Estimates of the Gamma Function Involving the PSI Function ⋮ Representations of hypergeometric functions for arbitrary parameter values and their use ⋮ Supplements to a class of logarithmically completely monotonic functions associated with the gamma function ⋮ Monotonicity properties of \(q\)-digamma and \(q\)-trigamma functions ⋮ An infinite class of completely monotonic functions involving the \(q\)-gamma function ⋮ Some monotonicity properties of gamma and \(q\)-gamma functions ⋮ Three classes of logarithmically completely monotonic functions involving gamma and psi functions ⋮ Bounds for the ratio of two gamma functions ⋮ A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums ⋮ Logarithmically completely monotonic functions relating to the gamma function ⋮ A function involving gamma function and having logarithmically absolute convexity ⋮ Monotonicity of some functions involving the gamma and psi functions ⋮ Completely monotonic ratios of basic and ordinary gamma functions ⋮ A class of logarithmically completely monotonic functions associated with the gamma function ⋮ A new asymptotic expansion of a ratio of two gamma functions and complete monotonicity for its remainder ⋮ Complete Monotonicity property for two functions related to the q-digamma function ⋮ Logarithmically complete monotonicity of ratios of \(q\)-gamma functions ⋮ Complete monotonicity and inequalities related to generalized \(k\)-gamma and \(k\)-polygamma functions ⋮ Hankel-total positivity of some sequences ⋮ Sharp bounds for a ratio of the \(q\)-gamma function in terms of the \(q\)-digamma function ⋮ Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions ⋮ Completely monotonic functions related to the q-gamma and the q-trigamma functions ⋮ Integral inequalities for some special functions ⋮ Completely monotonic gamma ratio and infinitely divisible H-function of Fox
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some classes of completely monotonic functions. II
- Completely monotonic functions associated with the gamma function and its q-analogues
- On Gautschi's harmonic mean inequality for the gamma function
- General inequalities, consequences and applications
- Inequalities generated by the gamma function
- An integral recursive inequality and applications
- Integral representation of some functions related to the gamma function
- Some completely monotonic functions involving polygamma functions and an application
- On Wallis' formula
- Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
- A Note on Gamma Functions
- On Some Gamma Function Inequalities
- On Gamma Function Inequalities
- On infinitely divisible matrices, kernels, and functions
- ON RAMANUJAN'S DOUBLE INEQUALITY FOR THE GAMMA FUNCTION
- Inequalities for the gamma function
- Inequalities and monotonicity properties for gamma and q-gamma functions
- ON A GAMMA FUNCTION INEQUALITY OF GAUTSCHI
- A Harmonic Mean Inequality for the Gamma Function
- On some inequalities for the gamma and psi functions
This page was built for publication: Completely monotonic functions involving the gamma and $q$-gamma functions
