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Article

Table in Gradshteyn and Ryzhik: Derivation of Definite Integrals of a Hyperbolic Function

Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada
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Author to whom correspondence should be addressed.
Academic Editor: Josef Mikeš
Received: 30 April 2021 / Revised: 15 September 2021 / Accepted: 8 October 2021 / Published: 20 October 2021
(This article belongs to the Special Issue Feature Papers 2021 Editors Collection)
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using special functions is their analytic continuation, which widens the range of the parameters of the definite integral over which the formula is valid. We give as examples definite integrals of logarithmic functions times a trigonometric function. In various cases these generalizations evaluate to known mathematical constants, such as Catalan’s constant C and π. View Full-Text
Keywords: entries in Gradshteyn and Rhyzik; lerch function; logarithm function; contour integral; Cauchy; infinite integral entries in Gradshteyn and Rhyzik; lerch function; logarithm function; contour integral; Cauchy; infinite integral
MDPI and ACS Style

Reynolds, R.; Stauffer, A. Table in Gradshteyn and Ryzhik: Derivation of Definite Integrals of a Hyperbolic Function. Sci 2021, 3, 37. https://doi.org/10.3390/sci3040037

AMA Style

Reynolds R, Stauffer A. Table in Gradshteyn and Ryzhik: Derivation of Definite Integrals of a Hyperbolic Function. Sci. 2021; 3(4):37. https://doi.org/10.3390/sci3040037

Chicago/Turabian Style

Reynolds, Robert, and Allan Stauffer. 2021. "Table in Gradshteyn and Ryzhik: Derivation of Definite Integrals of a Hyperbolic Function" Sci 3, no. 4: 37. https://doi.org/10.3390/sci3040037

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