Neville theta functions
In mathematics, the Neville theta functions, named after Eric Harold Neville, are defined as follows:
where: K(m) is the complete elliptic integral of the first kind, K'(m)=K(1-m), and is the elliptic nome.
Relationship to other functions
The Neville theta functions are related to the Jacobi elliptic functions. If pq(u,m) is a Jacobi elliptic function (p and q are one of s,c,n,d), then
Complex 3D plots
- Abramowitz and Stegun, pp. 578-579
- Neville (1944)
- wolfram Mathematic
- wolfram math
- Olver, F. W. J.; et al., eds. (2017-12-22). "NIST Digital Library of Mathematical Functions (Release 1.0.17)". National Institute of Standards and Technology. Retrieved 2018-02-26.
- Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.
- Neville, E. H. (Eric Harold) (1944). Jacobian Elliptic Functions. Oxford Clarendon Press.
- Weisstein, Eric W. "Neville Theta Functions". MathWorld.