Annales Mathématiques
Blaise Pascal

It is shown, that the function$$H\left(x\right)=\sum _{k=-\infty }^{\infty }{e}^{-k^{2}x}$$satisfies the relation$$H\left(x\right)=\sum _{n=0}^{\infty }\frac{{\left(2\pi \right)}^{2n}}{\left(2n\right)!}{H}^{\left(n\right)}\left(x\right).$$

DOI : https://doi.org/10.5802/ambp.332

@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/