Orr,s Theorem
المؤلف:
Bailey, W. N.
المصدر:
Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, 1935.
الجزء والصفحة:
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13-6-2019
1865
Orr's Theorem
If
 |
(1)
|
where 
is a hypergeometric function, then
 |
(2)
|
where 
is a Pochhammer symbol.
Furthermore, if
 |
(3)
|
then
 |
(4)
|
where 
is the gamma function (Bailey 1935, p. 84).
REFERENCES:
Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, 1935.
Edwards, D. "An Expansion in Factorials Similar to Vandermonde's Theorem, and Applications." Messenger Math. 52, 129-136, 1923.
Orr, W. M. "Theorems Relating to the Product of Two Hypergeometric Series." Trans. Cambridge Philos. Soc. 17, 1-15, 1899.
Watson, G. N. "The Theorems of Clausen and Cayley on Products of Hypergeometric Functions." Proc. London Math. Soc. 22, 163-170, 1924.
Whipple, F. J. W. "Algebraic Proofs of the Theorems of Cayley and Orr Concerning the Products of Certain Hypergeometric Series." J. London Math. Soc. 2, 85-90, 1927.
Whipple, F. J. W. "On a Formula Implied in Orr's Theorems Concerning the Products of Hypergeometric Series." J. London Math. Soc. 4, 48-50, 1929.
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