Geodesic
Integrals of logarithmic and hypergeometric functions
Communications in Mathematics, Tome 24 (2016) no. 1, pp. 7-22

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Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler sums. In this paper we explore many relations and explicitly derive closed form representations of integrals of logarithmic, hypergeometric functions and the Lerch phi transcendent in terms of zeta functions and sums of alternating harmonic numbers.
Classification : 05A10, 05A19, 11B83, 11M06, 11Y60, 33C20
Keywords: Logarithm function; Hypergeometric functions; Integral representation; Lerch transcendent function; Alternating harmonic numbers; Combinatorial series identities; Summation formulas; Partial fraction approach; Binomial coefficients. 
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Sofo, Anthony. Integrals of logarithmic and hypergeometric functions. Communications in Mathematics, Tome 24 (2016) no. 1, pp. 7-22. http://geodesic.mathdoc.fr/item/COMIM_2016__24_1_a1/