Addition formula for complementary error function with associated integral representations

摘要

In this paper, using the Mellin transform of parabolic cylinder functions we present an addition formula for the complementary error function in terms of the Gaussian func- tions. Also, some inverse Laplace transforms of the complementary error functions are shown and new integral representations for the exponential integral and Bessel functions are given. Moreover, the solution of di.usion equation in finite domain is presented in terms of the theta functions.