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

R. B. Paris

paper

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

arXiv:1405.3423

Abstract

We show how the asymptotic expansion for the gamma function $Γ (x)$ , 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.

arXiv comment9 pages, 0 figures

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

Abstract

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