A uniform asymptotic expansion for the incomplete gamma functions revisited

Abstract

A new uniform asymptotic expansion for the incomplete gamma function $\Gamma (a,z)$ valid for large values of $z$ was given by the author in {\it J. Comput. Appl. Math.} {\bf 148} (2002) 323--339. This expansion contains a complementary error function of an argument measuring transition across the point $z=a$, with easily computable coefficients that do not involve a removable singularity in the neighbourhood of this point. In this note we correct a misprint in the listing of certain coefficients in this expansion and discuss in more detail the situation corresponding to $\Gamma (a,a)$.

9 pages

References in corpus (1)

• The asymptotic expansion for the factorial and Lagrange inversion formula