The new properties of the theta functions
Annales Mathématiques Blaise Pascal, Tome 20 (2013) no. 2, pp. 391-398.

It is shown, that the function

H ( x ) = k = - e - k 2 x
satisfies the relation
H ( x ) = n = 0 ( 2 π ) 2 n ( 2 n ) ! H ( n ) ( x ) .

@article{AMBP_2013__20_2_391_0,
     author = {Czekalski, Stefan},
     title = {The new properties of the theta functions},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {391--398},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {20},
     number = {2},
     year = {2013},
     doi = {10.5802/ambp.332},
     mrnumber = {3138035},
     zbl = {1282.33030},
     language = {en},
     url = {www.numdam.org/item/AMBP_2013__20_2_391_0/}
}
Czekalski, Stefan. The new properties of the theta functions. Annales Mathématiques Blaise Pascal, Tome 20 (2013) no. 2, pp. 391-398. doi : 10.5802/ambp.332. http://www.numdam.org/item/AMBP_2013__20_2_391_0/

[1] Bellman, R. A Brief Introduction to Theta Functions, Hall, Rinehart and Winston, New York, 1961 | MR 125252 | Zbl 0098.28301

[2] Krazer, A. Lehrbuch der Theta - Funktionen, Chelsea, New York, 1971 | Zbl 0212.42901