Geodesic
Definite integral of logarithmic functions and powers in terms of the lerch function
Ural mathematical journal, Tome 7 (2021) no. 1, pp. 96-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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A family of generalized definite logarithmic integrals given by $$ \int_{0}^{1}\frac{\left(x^{ i m} (\log (a)+i \log (x))^k+x^{-i m} (\log (a)-i \log (x))^k\right)}{(x+1)^2}dx $$ built over the Lerch function has its analytic properties and special values listed in explicit detail. We use the general method as given in [5] to derive this integral. We then give a number of examples that can be derived from the general integral in terms of well known functions.
Keywords: entries of Gradshteyn and Ryzhik, Lerch function, Knuth's Series. 
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Robert Reynolds; Allan Stauffer. Definite integral of logarithmic functions and powers in terms of the lerch function. Ural mathematical journal, Tome 7 (2021) no. 1, pp. 96-101. http://geodesic.mathdoc.fr/item/UMJ_2021_7_1_a7/

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