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Ramanujan Cos/Cosh Identity


The amazing identity

 [1+2sum_(n=1)^infty(cos(ntheta))/(cosh(npi))]^(-2)+[1+2sum_(n=1)^infty(cosh(ntheta))/(cosh(npi))]^(-2)=(2Gamma^4(3/4))/pi

for all theta, where Gamma(z) is the gamma function. Equating coefficients of theta^0, theta^4, and theta^8 gives some amazing identities for the hyperbolic secant.


See also

Hyperbolic Secant

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Cite this as:

Weisstein, Eric W. "Ramanujan Cos/Cosh Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RamanujanCosCoshIdentity.html

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