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  is a polylogarithm,  is the gamma function, and  is the Hurwitz zeta function, and  is not a member of the real interval .

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

REFERENCES:

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 ." Bull. Soc. Math. France 17, 142-152, 1889.

Sondow, J. and Hadjicostas, P. "The Generalized-Euler-Constant Function  and a Generalization of Somos's Quadratic Recurrence Constant." 16 Oct 2006. http://arxiv.org/abs/math.CA/0610499.