• EllipticTheta[a, u, q]
The third argument of EllipticTheta should be a complex number with absolute value less than 1. This argument is the nome corresponding to the modulus employed by most other elliptic functions. See EllipticNomeQ.
The Jacobi elliptic functions (sn and friends) are often expressed in terms of theta functions, which can be computed very efficiently.
This is the derivative.