One Special Identity between the complete elliptic integrals of the first and the third kind

Yu Jia

I prove an identity between the first kind and the third kind complete elliptic integrals with the following form: $$Π({(1+x) (1-3 x)\over (1-x) (1+3 x)}, {(1+x)^3(1-3 x)\over (1-x…