Content deleted Content added
m Open access bot: doi updated in citation with #oabot. |
→Elliptic integral and elliptic nome: Fixed minor typo: "me" to "be" |
||
Line 216:
:<math>K(k) = \frac{\pi}{2}\sum_{a = 0}^{\infty} \frac{[(2a)!]^2}{16^{a}(a!)^4} k^{2a}</math>
An identical definition of the nome function can
:<math>\frac{1 - \sqrt[4]{1 - k^2}}{1 + \sqrt[4]{1 - k^2}} = \frac{\vartheta_{00}[q(k)] - \vartheta_{01}[q(k)]}{\vartheta_{00}[q(k)] + \vartheta_{01}[q(k)]} = \biggl[\sum_{n = 1}^{\infty} 2\,q(k)^{(2n - 1)^2}\biggr] \biggl[1 + \sum_{n = 1}^{\infty} 2\,q(k)^{4n^2}\biggr]^{-1}</math>
| |||