Definite Integral of Logarithmic Trigonometric Functions Expressed in terms of the Incomplete Gamma Function

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DOI:

https://doi.org/10.29020/nybg.ejpam.v14i4.4063

Keywords:

Incomplete gamma function, Meijer G function, Trigonometric function, Contour integral

Abstract

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 and π.

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How to Cite

Reynolds, R., & Stauffer, A. (2021). Definite Integral of Logarithmic Trigonometric Functions Expressed in terms of the Incomplete Gamma Function. European Journal of Pure and Applied Mathematics, 14(4), 1249–1265. https://doi.org/10.29020/nybg.ejpam.v14i4.4063

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