Jonquière,s Relation
المؤلف:
Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G.
المصدر:
Higher Transcendental Functions, Vol. 1. New York: Krieger
الجزء والصفحة:
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10-8-2019
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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 ![[0,1]](http://mathworld.wolfram.com/images/equations/JonquieresRelation/Inline5.gif)
.
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.
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