In mathematics, the Jacobi zeta function Z(u) is the logarithmic derivative of the Jacobi theta function ÃÂ(u). It is also commonly denoted as
Where E, K, and F are generic Incomplete Elliptical Integrals of the first and second kind. Jacobi Zeta Functions being kinds of Jacobi theta functions have applications to all their relevant fields and application. <br />
This relates Jacobi's common notation of, , , . to Jacobi's Zeta function.
Some additional relations include ,
References
- https://booksite.elsevier.com/samplechapters/9780123736376/Sample_Chapters/01~Front_Matter.pdf Pg.xxxiv
- http://mathworld.wolfram.com/JacobiZetaFunction.html