Geodesic
Logarithmic analog of Leibnitz series and some integrals connected with the Riemann zeta function
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 2, pp. 615-619

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A new expression for the analog of the Leibnitz series with alternating signs, which contains the multipliers depending on the logarithm of the term's number, is obtained. The values of some definite integrals connected with the above series are found. 
@article{FPM_2001_7_2_a16,
     author = {Yu. I. Babenko and A. I. Moshinskii},
     title = {Logarithmic analog of {Leibnitz} series and some integrals connected with the {Riemann} zeta function},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {615--619},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_2_a16/}
}
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Yu. I. Babenko; A. I. Moshinskii. Logarithmic analog of Leibnitz series and some integrals connected with the Riemann zeta function. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 2, pp. 615-619. http://geodesic.mathdoc.fr/item/FPM_2001_7_2_a16/