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Nielsen Generalized Polylogarithm


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.

The function reduces to the usual polylogarithm for the case

 S_(n-1,1)(z)=Li_n(z).

The Nielsen generalized polylogarithm is implemented as PolyLog[n, p, z].


See also

Polylogarithm

Related Wolfram sites

http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/PolyLog3/

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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 Polylogarithm

Cite this as:

Weisstein, Eric W. "Nielsen Generalized Polylogarithm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NielsenGeneralizedPolylogarithm.html

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