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Date: 18-7-2019
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Date: 7-8-2019
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Date: 13-8-2018
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N. Nielsen (1909) and Ramanujan (Berndt 1985) considered the integrals
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They found the values for and 2. The general constants for were found by Levin (1950) and, much later, independently by V. Adamchik (Finch 2003),
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where is the Riemann zeta function and is the polylogarithm. The first few values are
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REFERENCES:
Berndt, B. C. Ramanujan's Notebooks, Part I. New York: Springer-Verlag, 1985.
Borwein, J. M.; Bradley, D. M.; Broadhurst, D. J.; and Lisonek, P. "Special Values of Multidimensional Polylogarithms." Trans. Amer. Math. Soc. 353, 907-941, 2001.
Finch, S. R. "Apéry's Constant: Polylogarithms." §1.6.8 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 47-48, 2003.
Flajolet, P. and Salvy, B. "Euler Sums and Contour Integral Representation." Experim. Math. 7, 15-35, 1998.
Levin, V. I. "About a Problem of S. Ramanujan." Uspekhi Mat. Nauk 5, 161-166, 1950.
Nielsen, N. "Der Eulersche Dilogarithmus und seine Verallgemeinerungen." Nova Acta Leopoldina, Abh. der Kaiserlich Leopoldinisch-Carolinischen Deutschen Akad. der Naturforsch. 90, 121-212, 1909.
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