In mathematics, the Jacobi zeta function Z(u) is the logarithmic derivative of the Jacobi theta function Θ(u). It is also commonly denoted as [1]

[2]
[3]
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.
[1]
This relates Jacobi's common notation of, , , .[1] to Jacobi's Zeta function.
Some additional relations include ,
[1]
[1]
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References

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  1. ^ a b c d e f g Gradshteyn, Ryzhik, I.S., I.M. "Table of Integrals, Series, and Products" (PDF). booksite.com.{{cite web}}: CS1 maint: multiple names: authors list (link)
  2. ^ Abramowitz, Milton; Stegun, Irene A. (2012-04-30). Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Courier Corporation. ISBN 978-0-486-15824-2.
  3. ^ Weisstein, Eric W. "Jacobi Zeta Function". mathworld.wolfram.com. Retrieved 2019-12-02.