In mathematics, the Neville theta functions, named after Eric Harold Neville,[1] are defined as follows:[2][3]
[4]
where: K(m) is the complete elliptic integral of the first kind, , and is the elliptic nome.
Note that the functions θp(z,m) are sometimes defined in terms of the nome q(m) and written θp(z,q) (e.g. NIST[5]). The functions may also be written in terms of the τ parameter θp(z|τ) where .
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Relationship to other functions
The Neville theta functions may be expressed in terms of the Jacobi theta functions[5]
where .
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
Examples
Symmetry
Complex 3D plots
Notes
References
This page was last edited on 10 May 2024, at 04:34