Elliptic theta functions

[Asalex]

Dear All,

How can one solve the equation
$f_x=\sqrt{(1-f^2)(1-kf^2)}$
directly in terms of theta functions? I mean to introduce some associated Riemann surface, the associated theta functions, and to write down some identity?

Could you suggest some literature about it?

Thanks.

[пианист]

Интеграл (первого рода, емнис) в любой приличной книжке по предмету, в два счета гуглится.
В чем прикол?

[Brukvalub]

См. , например, Ахиезера и Мамфорда.