![sum_(n=0)^(infty)(-1)^n[((2n-1)!!)/((2n)!!)]^3](/images/equations/RamanujansHypergeometricIdentity/Inline1.svg) |  |  |
(1)
|
 |  |  |
(2)
|
 |  | ![[_2F_1(1/4,1/4; 1;-1)]^2](/images/equations/RamanujansHypergeometricIdentity/Inline9.svg) |
(3)
|
 |  |  |
(4)
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where 
is a hypergeometric
function, 
is a generalized
hypergeometric function, and 
is a gamma function.
Ramanujan's Hypergeometric Identity
See also
Generalized Hypergeometric Function, Hypergeometric FunctionExplore with Wolfram|Alpha
References
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, p. 106, 1999.Referenced on Wolfram|Alpha
Ramanujan's Hypergeometric IdentityCite this as:
Weisstein, Eric W. "Ramanujan's Hypergeometric Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RamanujansHypergeometricIdentity.html