I'm looking for an efficient implementation of the derivative of the first Jacobi theta function $\theta_1(z, \tau)$ or the derivative of its logarithm, which works with complex values of the variable and of the parameter. I implemented the algorithm given in Beebe's book for the derivative of the logarithm; it often works but there is a $\sin(2nz)$ which can becomes huge for $z$ complex, and then the algorithm fails in these cases.
2026-03-28 02:04:37.1774663477
Implementation of derivative of first Jacobi theta function
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