TOPICS
Neville Theta Functions
The functions
 |  |  | (1) |
 |  |  | (2) |
 |  |  | (3) |
 |  |  | (4) |
where
and
are theJacobi theta functions and
is the completeelliptic integral of the first kind.
The Neville theta functions are implemented in theWolfram Language asNevilleThetaC[z,m],NevilleThetaD[z,m],NevilleThetaN[z,m], andNevilleThetaS[z,m].
See also
Jacobi Theta FunctionsRelated Wolfram sites
http://functions.wolfram.com/EllipticFunctions/NevilleThetaC/,http://functions.wolfram.com/EllipticFunctions/NevilleThetaD/,http://functions.wolfram.com/EllipticFunctions/NevilleThetaN/,http://functions.wolfram.com/EllipticFunctions/NevilleThetaS/Explore with Wolfram|Alpha
More things to try:
References
Abramowitz, M. and Stegun, I. A. (Eds.). "Neville's Notation for Theta Functions." §16.36 inHandbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 578-579, 1972.Neville, E. H.Jacobi Elliptic Functions, 2nd ed. London: Oxford University Press, 1951.Referenced on Wolfram|Alpha
Neville Theta FunctionsCite this as:
Weisstein, Eric W. "Neville Theta Functions."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/NevilleThetaFunctions.html