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

Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
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Mathematics 2019, 7(12), 1148; https://doi.org/10.3390/math7121148
Received: 20 October 2019 / Revised: 20 November 2019 / Accepted: 21 November 2019 / Published: 24 November 2019
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. View Full-Text
Keywords: Mellin transform; logarithmic function; definite integral; Hankel contour; Cauchy integral; Bierens de Haan; Prudnikov Mellin transform; logarithmic function; definite integral; Hankel contour; Cauchy integral; Bierens de Haan; Prudnikov
MDPI and ACS Style

Reynolds, R.; Stauffer, A. A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function. Mathematics 2019, 7, 1148. https://doi.org/10.3390/math7121148

AMA Style

Reynolds R, Stauffer A. A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function. Mathematics. 2019; 7(12):1148. https://doi.org/10.3390/math7121148

Chicago/Turabian Style

Reynolds, Robert; Stauffer, Allan. 2019. "A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function" Mathematics 7, no. 12: 1148. https://doi.org/10.3390/math7121148

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