Monotonicity and inequalities for the gamma function
From MaRDI portal
Publication:1688520
DOI10.1186/s13660-017-1591-9zbMath1386.33003OpenAlexW2779947287WikidataQ59526007 ScholiaQ59526007MaRDI QIDQ1688520
Jing-Feng Tian, Zhen-Hang Yang
Publication date: 8 January 2018
Published in: Journal of Inequalities and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1186/s13660-017-1591-9
Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48)
Related Items (34)
An accurate approximation formula for gamma function ⋮ Monotonicity of the ratio of modified Bessel functions of the first kind with applications ⋮ Triple diamond-alpha integral and Hölder-type inequalities ⋮ Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric \(k\)-function ⋮ Windschitl type approximation formulas for the gamma function ⋮ Monotonicity rules for the ratio of two Laplace transforms with applications ⋮ Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function ⋮ Integral inequalities within the framework of generalized fractional integrals ⋮ Several integral inequalities for generalized Riemann-Liouville fractional operators ⋮ Improvements of generalized Hölder's inequalities and their applications ⋮ Increasing property and logarithmic convexity of two functions involving Dirichlet eta function ⋮ Some refinements of Hermite-Hadamard inequality using k-fractional Caputo derivatives ⋮ Monotonicity and inequalities involving the incomplete gamma function ⋮ Delta L'Hospital-, Laplace- and variable limit-type monotonicity rules on time scales ⋮ Some refinements of the Hermite-Hadamard inequality with the help of weighted integrals ⋮ Monotonicity of three kinds of functions involving the Gaussian hypergeometric function ⋮ Some extensions of the Hermite-Hadamard inequalities for quasi-convex functions via weighted integral ⋮ Hermite-Hadamard type inequalities via weighted integral operators ⋮ Bounds for the perimeter of an ellipse in terms of power means ⋮ Two asymptotic expansions for gamma function developed by Windschitl's formula ⋮ A comparison theorem for two divided differences and applications to special functions ⋮ Sharp Smith's bounds for the gamma function ⋮ A class of completely mixed monotonic functions involving the gamma function with applications ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ New properties of the divided difference of psi and polygamma functions ⋮ A new asymptotic expansion of a ratio of two gamma functions and complete monotonicity for its remainder ⋮ Logarithmically complete monotonicity of ratios of \(q\)-gamma functions ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions ⋮ Monotonicity and inequalities involving the modified Bessel functions of the second kind ⋮ On Burnside type approximation for the gamma function ⋮ Decreasing properties of two ratios defined by three and four polygamma functions ⋮ Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions ⋮ Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function ⋮ A class of strongly completely monotonic functions related to gamma function
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A more accurate approximation for the gamma function
- Approximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma function
- Some new asymptotic approximations of the gamma function based on Nemes' formula, Ramanujan's formula and Burnside's formula
- Two families of approximations for the gamma function
- Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function
- Ramanujan's estimate for the gamma function via monotonicity arguments
- Improved asymptotic formulas for the gamma function
- Asymptotic formulas for gamma function with applications
- On non-monotonic ageing properties from the Laplace transform, with actuarial applications
- A new fast asymptotic series for the gamma function
- New asymptotic expansion for the gamma function
- Inequalities for the gamma function
- An ultimate extremely accurate formula for approximation of the factorial function
- Some properties of the divided difference of psi and polygamma functions
- A new sharp approximation for the gamma function related to Burnside's formula
- Monotonicity criterion for the quotient of power series with applications
- A new asymptotic series for the gamma function
- The special functions and their approximations. Vol. I, II
- A refinement of a double inequality for the gamma function
- SHARP INEQUALITIES FOR FACTORIAL n
- Decision procedure for indefinite hypergeometric summation
- Necessary and Sufficient Conditions for the Representation of a Function as a Laplace Integral
- Monotonicity and sharp inequalities related to gamma function
- Properties and refinements of Aczél-type inequalities
- Properties of generalized sharp Hölder's inequalities
- On some inequalities for the gamma and psi functions
This page was built for publication: Monotonicity and inequalities for the gamma function