A Note on a Triple Integral

Abstract

A closed form expression for a triple integral not previously considered is derived, in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. The kernel of the integral involves the product of the logarithmic, exponential, quotient radical, and polynomial functions. Special cases are derived in terms of fundamental constants; results are summarized in a table. All results in this work are new.

Keywords

• triple integral
• Lerch function
• Catalan’s constant
• Apéry’s constant
• Euler’s constant
• Glaisher’s constant