On the approximation of the lower generalized incomplete gamma function arising in heat conduction problems

Abstract EN

rn this paper we consider the lower generalized incomplete gamma function 7(a,x; &) = / ;-zr > 0, Re6 > 0,6 ^ 0 Jo where the parameter a can be any real number except for zero or negative integers.

Several expansions and approximations are obtained using known special functions.

We study also the case when b = -ico for periodic boundary conditions.

Closed form expressions are also given for positive and negative half integer values of a.