Jonquière's Relation

Jonquière's relation, sometimes also spelled "Joncquière's relation" (Erdélyi et al. 1981, p. 31), states


Erdélyi et al. (1981, p. 31), where Li_s(z) is a polylogarithm, Gamma(s) is the gamma function, and zeta(s,w) is the Hurwitz zeta function, and z is not a member of the real interval [0,1].

The most general form of the identity valid everywhere in the complex plane is


See also


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Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 1. New York: Krieger, p. 31, 1981.Jonquière, A. "Note sur la série sum_(n=1)^(n=infty)(x^n)/(n^s)." Bull. Soc. Math. France 17, 142-152, 1889.Sondow, J. and Hadjicostas, P. "The Generalized-Euler-Constant Function gamma(z) and a Generalization of Somos's Quadratic Recurrence Constant." 16 Oct 2006.

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Jonquière's Relation

Cite this as:

Weisstein, Eric W. "Jonquière's Relation." From MathWorld--A Wolfram Web Resource.

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