Computation of Jacobi Theta functions

[did oslo]

Hi, 

I am looking for the state of the art of efficient accurate computations 

of the classical Jacobian Theta functions, specially in high precision 

computations,  

I am asking because I may have derived such an algorithm but, since I am 

not at all an expert in this field, I do not know where to look for comparisons. 

(I found nothing relevant for me in NIST, Abramowitz & Stegun, Wikipedia 

and other references therein.) 

The approach might be extendable to more general Theta functions 

(e.g. multi-dimensional) but I don't want to waste my time if I am 

reinventing the wheel, or inventing a bad wheel ;-) Hence my request. 

Thanks for the tips,

Did

[Edgar Costa]

https://arxiv.org/abs/2505.22382