A generalization of the polylogarithm function defined by
![S_(n,p)(z)=((-1)^(n+p-1))/((n-1)!p!)int_0^1((lnt)^(n-1)[ln(1-zt)]^p)/tdt.](/images/equations/NielsenGeneralizedPolylogarithm/NumberedEquation1.svg) |
The function reduces to the usual polylogarithm for the case
 |
The Nielsen generalized polylogarithm is implemented as PolyLog[n, p, z].
Nielsen Generalized Polylogarithm
See also
PolylogarithmRelated Wolfram sites
http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/PolyLog3/Explore with Wolfram|Alpha
References
Kölbig, K. S. "Nielsen's Generalized Polylogarithms." SIAM J. Math. Anal. 17, 1232-1258, 1986.Wolfram, S. The Mathematica Book, 5th ed. Champaign, IL: Wolfram Media, pp. 772-773, 2003.Referenced on Wolfram|Alpha
Nielsen Generalized PolylogarithmCite this as:
Weisstein, Eric W. "Nielsen Generalized Polylogarithm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NielsenGeneralizedPolylogarithm.html