On the asymptotic expansion of $\Gamma(x)$, Lagrange's inversion theorem and the Stirling coefficients

R. B. Paris

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arXiv · 1405.3423

On the asymptotic expansion of $\Gamma(x)$, Lagrange's inversion theorem and the Stirling coefficients

R. B. Paris

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Abstract

We show how the asymptotic expansion for the gamma function $\Gamma(x)$, similar to that obtained by Boyd [Proc. Roy. Soc. London A447 (1994) 609--630], can be obtained by using a form of Lagrange's inversion theorem with a remainder. A (possibly) new closed-form representation for the Stirling coefficients is given.

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R. B. Paris. 2014-05-14. On the asymptotic expansion of $\Gamma(x)$, Lagrange's inversion theorem and the Stirling coefficients. https://arxiv.org/abs/1405.3423

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