Definite integral of a hyperbolic quotient function expressed in terms of the Lerch function

Robert Reynolds, Allan Stauffer

Abstract

In applied sciences it is always useful to improve the catalogue of definite integrals available in tables. In this paper the authors derived definite integrals used in research concerned with perturbation analysis of single Langmuir solitons, proving the Riemann Hypothesis and the Goldbach conjecture and the LPM effect in sequential bremsstrahlung. We also derived new results and summarized these formulae in a table of integrals.

Keywords

entries in Gradshteyn and Ryzhik; Mellin transform; Hyperbolic function; Definite integral; Catalan's constant

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