Derivation of Logarithmic and Logarithmic Hyperbolic Tangent Integrals Expressed in Terms of Special Functions

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, 2020, vol. 8, issue 5, 1-6

Abstract: The derivation of integrals in the table of Gradshteyn and Ryzhik in terms of closed form solutions is always of interest. We evaluate several of these definite integrals of the form ∫ 0 ∞ log ( 1 ± e − α y ) R ( k , a , y ) d y in terms of a special function, where R ( k , a , y ) is a general function and k , a and α are arbitrary complex numbers, where R e ( α ) > 0 .

Keywords: Aton Winckler; hyperbolic tangent; logarithmic function; definite integral; hankel contour; Cauchy integral; Gradshteyn and Ryzhik; Bierens de Haan (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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