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](/images/equations/RamanujanCosCoshIdentity/NumberedEquation1.svg) |
for all 
,
where 
is the gamma function. Equating coefficients of
,
,
and 
gives some amazing identities for the hyperbolic
secant.
Ramanujan Cos/Cosh Identity
See also
Hyperbolic SecantExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Ramanujan Cos/Cosh Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RamanujanCosCoshIdentity.html