A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function

Robert Reynolds and Allan Stauffer
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Robert Reynolds: Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
Allan Stauffer: Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada

Mathematics, 2019, vol. 7, issue 12, 1-5

Abstract: We present a method using contour integration to evaluate the definite integral of the form ∫ 0 ∞ log k ( a y ) R ( y ) d y in terms of special functions, where R ( y ) = y m 1 + α y n and k , m , a , α and n are arbitrary complex numbers. We use this method for evaluation as well as to derive some interesting related material and check entries in tables of integrals.

Keywords: Mellin transform; logarithmic function; definite integral; Hankel contour; Cauchy integral; Bierens de Haan; Prudnikov (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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