Re: [math-fun] moRe: EllipticE valuation [Was: EllipticK valuation [Was: Elliptic K π approximation]]

* Bill Gosper <billgosper@gmail.com> [Nov 12. 2012 16:42]:

On Wed, Nov 7, 2012 at 3:05 PM, Bill Gosper <billgosper@gmail.com> wrote: [...]

In http://oeis.org/A194094 Michael Somos gives: (2/Pi)*elliptic_E(k) = theta_3(q)^2 - 2 * (theta_4(q) / theta_3(q))^2 * Dq ( theta_4(q)^-2 ) = theta_3(q)^2 + 4 Dq (theta_4(q)) / (theta_4(q) * theta_3(q)^2) where Dq (f) := q * df/dq