A Quadruple Integral Involving Product of the Struve <i><b>H</b>_v</i>(<i>β</i><i>t</i>) and Parabolic Cylinder <i>D_u</i>(<i>α</i><i>x</i>) Functions

Abstract

The objective of the present paper is to obtain a quadruple infinite integral. This integral involves the product of the Struve and parabolic cylinder functions and expresses it in terms of the Hurwitz–Lerch Zeta function. Almost all Hurwitz-Lerch Zeta functions have an asymmetrical zero distributionSpecial cases in terms fundamental constants and other special functions are produced. All the results in the work are new.

Keywords

• Struve function
• parabolic cylinder function
• quadruple integral
• Hurwitz–Lerch Zeta function
• Catalan’s constant
• Apéry’s constant