Abstract

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 functions. 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 diffusion equation in finite domain is presented in terms of the theta functions.

Keywords: addition formula; Mellin transform; Laplace transform; complementary error function; Theta function.

MSC: 33B20, 44A10

Pages:  287$-$297     

Volume  68 ,  Issue  4 ,  2016