See also
Elliptic Integral of the First Kind,
Elliptic Integral
of the Second Kind,
Heuman Lambda Function,
Zeta Function
Related Wolfram sites
http://functions.wolfram.com/EllipticIntegrals/JacobiZeta/
Explore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, p. 595, 1972.Gradshteyn, I. S. and Ryzhik,
I. M. Tables
of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press,
2000.Tölke, F. "Jacobische Zeta- und Heumansche Lambda-Funktionen."
§132 in Praktische
Funktionenlehre, dritter Band: Jacobische elliptische Funktionen, Legendresche elliptische
Normalintegrale und spezielle Weierstraßsche Zeta- und Sigma Funktionen.
Berlin: Springer-Verlag, pp. 94-99, 1967.Referenced on Wolfram|Alpha
Jacobi Zeta Function
Cite this as:
Weisstein, Eric W. "Jacobi Zeta Function."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JacobiZetaFunction.html
Subject classifications
or 
.
is the Jacobi amplitude, 
is the parameter, and 
and 
are elliptic
integrals of the first kind, and 
is an elliptic
integral of the second kind. See Gradshteyn and Ryzhik (2000, p. xxxi) for
expressions in terms of theta functions. The Jacobi zeta functions is implemented
in the Wolfram Language as JacobiZeta[phi,
m].
