Abstract

We consider the complex zeros with respect to z of the incomplete gamma functions fl(a; z) and \Gamma(a; z), with a real and positive. In particular we are interested in the case that a is large. The zeros are obtained from approximations that are computed by using uniform asymptotic expansions of the incomplete gamma functions. The complex zeros of the complementary error function are used as a first approximations. Applications are discussed for the zeros of the partial sums s n (z) = P n j=0 z j =j! of exp(z). 1991 Mathematics Subject Classification: 33B15, 33B20, 41A60, 65U05. Keywords & Phrases: incomplete gamma functions, zeros of incomplete gamma functions, error function, uniform asymptotic expansion. 1.

Citations