A Quadruple Integral Involving Chebyshev Polynomials <i>T_n</i>(<i>x</i>): Derivation and Evaluation

Abstract

The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) and derive in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. The zero distribution of almost all Hurwitz-Lerch zeta functions is asymmetrical. All the results in this work are new.

Keywords

• Chebyshev polynomial
• quadruple integral
• Hurwitz-Lerch zeta function
• Apéry’s constant