A quintuple integral involving the product of Hermite polynomial Hn(βx) and parabolic cylinder function Dv(αt): derivation and evaluation

Abstract

In this paper, we derive an integral transform involving the product of Hermite polynomial $ H_{n}(\beta x) $ and parabolic cylinder function $ D_{v}(\alpha t) $. These integral transforms will be evaluated in terms of Lerch function. Various formulae are also evaluated in terms of special functions to complete this paper. All the results in this paper are new.

Keywords

• parabolic cylinder function
• quintuple integral
• lerch function
• cauchy integral