TOPICS
Search

Neville Theta Functions

The Neville theta functions are the four functions defined by

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

where H(u) and Theta(u) are the Jacobi theta functions with the same fixed elliptic modulus k, and K=K(k) 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

https://functions.wolfram.com/EllipticFunctions/NevilleThetaC/, https://functions.wolfram.com/EllipticFunctions/NevilleThetaD/, https://functions.wolfram.com/EllipticFunctions/NevilleThetaN/, https://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, England: Oxford University Press, 1951.

Referenced on Wolfram|Alpha

Neville Theta Functions

Cite this as:

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

Subject classifications