On Wallis' formula
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Publication:3235901
DOI10.1017/S095018430000029XzbMath0072.28401OpenAlexW2324627482MaRDI QIDQ3235901
Publication date: 1956
Published in: Edinburgh Mathematical Notes (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s095018430000029x
Related Items (30)
Estimates for Wallis' ratio and related functions ⋮ Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ Complete monotonicity of divided differences of the di- and tri-gamma functions with applications ⋮ Complete monotonicity of two functions involving the tri- and tetra-gamma functions ⋮ Integral representations of the Catalan numbers and their applications ⋮ On the quantum mechanical derivation of the Wallis formula for \textit{ {\(\pi\)}} ⋮ Integral representations, monotonic properties, and inequalities on extended central binomial coefficient ⋮ An asymptotic approximation of Wallis' sequence ⋮ Completely monotone functions and the Wallis ratio ⋮ Efficient homomorphic comparison methods with optimal complexity ⋮ Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications ⋮ Bounds for the ratio of two gamma functions -- from Wendel's and related inequalities to logarithmically completely monotonic functions ⋮ Weighted inequalities and negative binomials ⋮ The monotonicity and convexity for the ratios of modified Bessel functions of the second kind and applications ⋮ Unnamed Item ⋮ Bounds for the ratio of two gamma functions: from Wendel's asymptotic relation to Elezović-Giordano-Pečarić's theorem ⋮ Gurland's ratio for the gamma function ⋮ A simple asymptotic estimate of Wallis' ratio using Stirling's factorial formula ⋮ REGULARIZED LEAST SQUARE REGRESSION WITH SPHERICAL POLYNOMIAL KERNELS ⋮ An Improper Integral, the Beta Function, the Wallis Ratio, and the Catalan Numbers ⋮ Completely monotonic functions involving the gamma and $q$-gamma functions ⋮ Complete monotonicity and inequalites involving Gurland's ratios of gamma functions ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions ⋮ Inequalities for ultraspherical polynomials and the gamma function ⋮ Unnamed Item ⋮ Sharp Inequalities for Polygamma Functions ⋮ Basic asymptotic estimates for powers of Wallis’ ratios ⋮ Simple accurate balanced asymptotic approximation of Wallis' ratio using Euler-Boole alternating summation
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