On the Power Series Expansion of the Reciprocal Gamma Function

Lazhar Fekih-Ahmed (1)

1 ENIT - Ecole Nationale d'Ingénieurs de Tunis

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.

Mots clés: Special functions; Reciprocal Gamma function; Taylor expansion; asymptotic expansion

Domaines: Théorie des nombres [math.NT]; Mathématiques générales [math.GM]

Lazhar Fekih-Ahmed. On the Power Series Expansion of the Reciprocal Gamma Function. 2014. ⟨hal-01029331v4⟩