Some New Properties of the Gamma Function Based on Ramanujan’s Formula and Nemes’ Formula
Preprint
- 27 February 2026
- preprint
- Published by MDPI AG in Preprints.org
Abstract
Ramanujan presented the following approximation formula of the gamma function: \( \Gamma(x+1)\approx\sqrt{\pi}\left( \frac{x}{e}\right) ^{x} \left( 8x^{3}+4x^{2}+x+\frac{1}{30}\right) ^{1/6},\qquad x\to\infty. \) In this paper, we develop Ramanujan's approximation formula to derive a number of complete asymptotic expansions. We also establish several subadditive and superadditive properties of some functions which are related to the gamma function.
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