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