Annales Mathématiques
Blaise Pascal
no. 2
The new properties of the theta functions
Stefan Czekalski1
1 Ul. Marszalkowska 1 m 80 00-624 Warszawa Poland
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 ) .

DOI : 10.5802/ambp.332

Stefan Czekalski 1

1 Ul. Marszalkowska 1 m 80 00-624 Warszawa Poland 
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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/articles/10.5802/ambp.332/

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

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

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