Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions

DOI10.1016/j.cam.2011.01.045zbMath1225.33002OpenAlexW2028074687MaRDI QIDQ535461

Tomislav Burić, Neven Elezović

Publication date: 11 May 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.01.045

zbMATH Keywords

gamma functionasymptotic expansionBernoulli polynomialsStirling formulaWallis power functionWallis quotient

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation to limiting values (summation of series, etc.) (40A25) Numerical approximation and evaluation of special functions (33F05)

Related Items (18)

Asymptotic expansions of integral means and applications to the ratio of gamma functions ⋮ New asymptotic expansions of the quotient of gamma functions ⋮ Estimations of psi function and harmonic numbers ⋮ Appell polynomials and asymptotic expansions ⋮ A double inequality for the Apéry constant ⋮ Simple, accurate, asymptotic estimates for the ratio of two gamma functions ⋮ Bounds for the ratio of two gamma functions: from Wendel's asymptotic relation to Elezović-Giordano-Pečarić's theorem ⋮ A simple asymptotic estimate of Wallis' ratio using Stirling's factorial formula ⋮ Monotonicity properties related to the ratio of two gamma functions ⋮ On the asymptotics of the rescaled Appell polynomials ⋮ Some properties of a sequence arising from geometric probability for pairs of hyperplanes intersecting with a convex body ⋮ Generalized Bernoulli polynomials and numbers, revisited ⋮ Asymptotic expansions of the binomial coefficients ⋮ A new asymptotic expansion of a ratio of two gamma functions and complete monotonicity for its remainder ⋮ Asymptotic formulae associated with the Wallis power function and digamma function ⋮ Asymptotic expansions of the gamma function and Wallis function through polygamma functions ⋮ Basic asymptotic estimates for powers of Wallis’ ratios ⋮ Simple accurate balanced asymptotic approximation of Wallis' ratio using Euler-Boole alternating summation

Cites Work

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• The asymptotic series of the generalized Stirling formula
• New approximation formulas for evaluating the ratio of gamma functions
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• Two new asymptotic expansions of the ratio of two gamma functions
• A new asymptotic series for the gamma function
• The special functions and their approximations. Vol. I, II
• The asymptotic expansion of a ratio of gamma functions
• Error Bounds for Asymptotic Expansions of the Ratio of Two Gamma Functions
• A new method for establishing and proving accurate bounds for the Wallis ratio
• Stirling's formula revisited via some classical and new inequalities
• The best bounds in Gautschi's inequality
• The best bounds in Wallis’ inequality
• A Note on the Asymptotic Expansion of a Ratio of Gamma Functions

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