It is shown, that the functionsatisfies the relation
@article{AMBP_2013__20_2_391_0, author = {Czekalski, Stefan}, title = {The new properties of the theta functions}, journal = {Annales Math\'ematiques Blaise Pascal}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {20}, number = {2}, year = {2013}, pages = {391-398}, doi = {10.5802/ambp.332}, mrnumber = {3138035}, zbl = {1282.33030}, language = {en}, url = {https://ambp.centre-mersenne.org/item/AMBP_2013__20_2_391_0} }
Czekalski, Stefan. The new properties of the theta functions. Annales Mathématiques Blaise Pascal, Volume 20 (2013) no. 2, pp. 391-398. doi : 10.5802/ambp.332. https://ambp.centre-mersenne.org/item/AMBP_2013__20_2_391_0/
[1] A Brief Introduction to Theta Functions, Hall, Rinehart and Winston, New York (1961) | MR 125252 | Zbl 0098.28301
[2] Lehrbuch der Theta - Funktionen, Chelsea, New York (1971) | Zbl 0212.42901