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Cayley's Hypergeometric Function Theorem

Cayley's hypergeometric function theorem states that if

(1-z)^(a+b-c)_2F_1(2a,2b;2c;z)=sum_(n=0)^inftya_nz^n,

then

_2F_1(a,b;c+1/2;z)_2F_1(c-a,c-b;c1/2;z)=sum_(n=0)^infty((c)_n)/((c+1/2))a_nz^n,

where (a)_n is a Pochhammer symbol and _2F_1(a,b;c;z) is a hypergeometric function.

See also

Generalized Hypergeometric Function, Hypergeometric Function, Orr's Theorem

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References

Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, 1935.Cayley, A. "On a Theorem Relating to Hypergeometric Series." Philos. Mag. 16, 356-357, 1858. Reprinted in Collected Papers, Vol. 3, pp. 268-269.

Referenced on Wolfram|Alpha

Cayley's Hypergeometric Function Theorem

Cite this as:

Weisstein, Eric W. "Cayley's Hypergeometric Function Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CayleysHypergeometricFunctionTheorem.html

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