The functions

			(1)
			(2)
			(3)
			(4)

where and are the Jacobi theta functions and is the complete elliptic integral of the first kind.

The Neville theta functions are implemented in Mathematica as NevilleThetaC[z, m], NevilleThetaD[z, m], NevilleThetaN[z, m], and NevilleThetaS[z, m].

RELATED 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/

Abramowitz, M. and Stegun, I. A. (Eds.). "Neville's Notation for Theta Functions." §16.36 in Handbook 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.

CITE THIS AS:

Weisstein, Eric W. "Neville Theta Functions." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NevilleThetaFunctions.html