The new properties of the theta functions

Stefan Czekalski

doi:10.5802/ambp.332

Stefan Czekalski

Annales Mathématiques Blaise Pascal, Tome 20 (2013) no. 2, pp. 391-398.

Résumé

It is shown, that the function

\begin{matrix} H (x) & = \sum_{k = - \infty}^{\infty} e^{- k^{2} x} \\ satisfies the relation \\ H (x) & = \sum_{n = 0}^{\infty} \frac{{(2 π)}^{2 n}}{(2 n)!} H^{(n)} (x) . \end{matrix}

MR 3138035 | Zbl 1282.33030

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

@article{AMBP_2013__20_2_391_0,
     author = {Stefan Czekalski},
     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},
     zbl = {1282.33030},
     mrnumber = {3138035},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2013__20_2_391_0/}
}

Stefan Czekalski. The new properties of the theta functions. Annales Mathématiques Blaise Pascal, Tome 20 (2013) no. 2, pp. 391-398. doi : 10.5802/ambp.332. https://ambp.centre-mersenne.org/item/AMBP_2013__20_2_391_0/

Bibliographie

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

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