More accurate approximations for the Gamma function
Gerg\H{o} Nemes
TL;DR
This paper introduces new, highly accurate approximation formulas for the Gamma function, inspired by series transformations and asymptotic expansions related to binomial coefficients.
Contribution
It presents novel approximation methods for the Gamma function based on series transformations and asymptotic analysis, improving accuracy over existing formulas.
Findings
New approximation formulas for the Gamma function
Enhanced accuracy compared to previous methods
Inspired by Gosper's formula and binomial coefficient expansions
Abstract
A series transformation idea inspired by a formula of R. W. Gosper and some asymptotic expansions for the central binomial coefficients leads us to new accurate approximations for the Gamma function.
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Taxonomy
TopicsMathematical functions and polynomials · Mathematical Inequalities and Applications · Matrix Theory and Algorithms