Neville theta functions

In mathematics, the Neville theta functions, named after Eric Harold Neville, are defined as follows:
where: K is the complete elliptic integral of the first kind,, and is the elliptic nome.
Note that the functions θ_p are sometimes defined in terms of the nome q and written θ_p. The functions may also be written in terms of the τ parameter θ_p where.

Relationship to other functions

The Neville theta functions may be expressed in terms of the Jacobi theta functions
where.
The Neville theta functions are related to the Jacobi elliptic functions. If pq is a Jacobi elliptic function, then