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Neville Theta Functions

The functions

theta_s(u)=(H(u))/(H^'(0))
(1)
theta_d(u)=(Theta(u+K))/(Theta(k))
(2)
theta_c(u)=(H(u))/(H(K))
(3)
theta_n(u)=(Theta(u))/(Theta(0)),
(4)

where H(u) and Theta(u) are the Jacobi theta functions and K(u) is the complete elliptic integral of the first kind.

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

See also

Jacobi Theta Functions

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/

Explore with Wolfram|Alpha

References

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.

Referenced on Wolfram|Alpha

Neville Theta Functions

Cite this as:

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

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