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تسجيل

G-Function

المؤلف:  Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G

المصدر:  The Function G(z)." §1.8 in Higher Transcendental Functions, Vol. 1. New York: Krieger,

الجزء والصفحة:  pp. 20 and 44-46

8-8-2019

2018

G-Function

Min   Max       Re       Im

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

			(2)
			(3)

for .  is also given by the series

(4)

and in terms of the hypergeometric function by

(5)

It obeys the functional relations

			(6)
			(7)
		{-2/msum_(r=0)^(m-1)(-1)^rpsi_0(z+r/m) for m even; 1/msum_(r=0)^(m-1)(-1)^rG(z+r/m) for m odd." src="http://mathworld.wolfram.com/images/equations/G-Function/Inline19.gif" style="height:104px; width:222px" />	(8)

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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.