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Slater,s Formula

المؤلف:  Slater, L. J.

المصدر:  "An Elementary Proof of the _4F_3[1] Summation Theorem." §2.7.1 in Confluent Hypergeometric Functions. Cambridge, England: Cambridge University Press

الجزء والصفحة:  p. 31

18-6-2019

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Slater's Formula

Slater (1960, p. 31) terms the identity

 

for  a nonnegative integer the " summation theorem." Here,  is a generalized hypergeometric function with argument  and  is a Pochhammer symbol.

This is a special case of the more general identity

which holds for  (O. Marichev, pers. comm., May 16, 2008).

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REFERENCES:

Slater, L. J. "An Elementary Proof of the  Summation Theorem." §2.7.1 in Confluent Hypergeometric Functions. Cambridge, England: Cambridge University Press, p. 31, 1960.