As defined by Erdélyi et al. (1981, p. 20), the -function is given by
(1)
where is the digamma
function . Integral representations are given by
for . is also given by the series
(4)
and in terms of the hypergeometric function
by
(5)
It obeys the functional relations
See also Barnes G-Function ,
Digamma Function ,
Meijer G-Function ,
Ramanujan
g - and G-Functions
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References Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. "The Function ." §1.8 in Higher
Transcendental Functions, Vol. 1. New York: Krieger, pp. 20 and
44-46, 1981. Referenced on Wolfram|Alpha G-Function
Cite this as:
Weisstein, Eric W. "G-Function." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/G-Function.html
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