Nielsen-Ramanujan Constants
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
N. Nielsen (1909) and Ramanujan (Berndt 1985) considered the integrals
 | (1) |
and 2. The general constants for 
were found by V. Adamchik (Finch) | (2) |
is the Riemann Zeta Function and 
is the Polylogarithm. The first few values are |  |  | (3) |
 | |  | (4) |
 | |  | (5) |
 | |  | (6) |
See also Polylogarithm, Riemann Zeta Function
References
Berndt, B. C. Ramanujan's Notebooks, Part I. New York: Springer-Verlag, 1985. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/nielram/nielram.html Flajolet, P. and Salvy, B. ``Euler Sums and Contour Integral Representation.'' Submitted to Experim. Math 1997. http://pauillac.inria.fr/algo/flajolet/Publications/publist.html.
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