On the Power Series Expansion of the Reciprocal Gamma Function
Number Theory
2017-01-16 v4
Abstract
Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values of the indices. Both the sign oscillations and the leading order of growth are given.
Keywords
Cite
@article{arxiv.1407.5983,
title = {On the Power Series Expansion of the Reciprocal Gamma Function},
author = {Lazhar Fekih-Ahmed},
journal= {arXiv preprint arXiv:1407.5983},
year = {2017}
}
Comments
Corrected a sign in equation (3.21) due to a minor error in (3.19) where the fraction was inadvertently inverted. Now the rough approximation provides an elementary proof that the order of the reciprocal gamma function is 1 and that its type is maximal