Neville theta functions

Summary

The Neville theta functions $\theta_s$, $\theta_c$, $\theta_d$, $\theta_n$ are rescaled Jacobi theta functions. Their argument is the argument $u$ of the Jacobi elliptic functions. With this normalisation the Jacobi functions are simple quotients: $\operatorname{sn} = \theta_s/\theta_n$, $\operatorname{cn} = \theta_c/\theta_n$ and $\operatorname{dn} = \theta_d/\theta_n$. The letters $s, c, d, n$ match the letters in the names of the twelve Jacobi functions, so any Jacobi function $\operatorname{pq}$ is $\theta_p/\theta_q$.