The new properties of the theta functions

• [1] Ul. Marszalkowska 1 m 80 00-624 Warszawa Poland
• Volume: 20, Issue: 2, page 391-398
• ISSN: 1259-1734

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Abstract

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It is shown, that the function$\begin{array}{cc}\hfill H\left(x\right)& =\sum _{k=-\infty }^{\infty }{e}^{-{k}^{2}x}\hfill \\ \multicolumn{2}{c}{\text{satisfies}\phantom{\rule{4pt}{0ex}}\text{the}\phantom{\rule{4pt}{0ex}}\text{relation}}\\ \hfill H\left(x\right)& =\sum _{n=0}^{\infty }\frac{{\left(2\pi \right)}^{2n}}{\left(2n\right)!}{H}^{\left(n\right)}\left(x\right).\hfill \end{array}$

How to cite

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Czekalski, Stefan. "The new properties of the theta functions." Annales mathématiques Blaise Pascal 20.2 (2013): 391-398. <http://eudml.org/doc/275550>.

@article{Czekalski2013,
abstract = {It is shown, that the function\begin\{align*\} H(x) &= \sum \limits \_\{k=-\infty \}^\infty e^\{-k^\{2\}x\}\\ \multicolumn\{2\}\{l\}\{\text\{satisfies the relation\}\}\\ H(x) &= \sum \limits \_\{n=0\}^\infty \{(2\pi )^\{2n\}\over (2n)!\}H^\{(n)\}(x). \end\{align*\}},
affiliation = {Ul. Marszalkowska 1 m 80 00-624 Warszawa Poland},
author = {Czekalski, Stefan},
journal = {Annales mathématiques Blaise Pascal},
keywords = {theta functions; series},
language = {eng},
month = {7},
number = {2},
pages = {391-398},
publisher = {Annales mathématiques Blaise Pascal},
title = {The new properties of the theta functions},
url = {http://eudml.org/doc/275550},
volume = {20},
year = {2013},
}

TY - JOUR
AU - Czekalski, Stefan
TI - The new properties of the theta functions
JO - Annales mathématiques Blaise Pascal
DA - 2013/7//
PB - Annales mathématiques Blaise Pascal
VL - 20
IS - 2
SP - 391
EP - 398
AB - It is shown, that the function\begin{align*} H(x) &= \sum \limits _{k=-\infty }^\infty e^{-k^{2}x}\\ \multicolumn{2}{l}{\text{satisfies the relation}}\\ H(x) &= \sum \limits _{n=0}^\infty {(2\pi )^{2n}\over (2n)!}H^{(n)}(x). \end{align*}
LA - eng
KW - theta functions; series
UR - http://eudml.org/doc/275550
ER -

References

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1. R. Bellman, A Brief Introduction to Theta Functions, (1961), Hall, Rinehart and Winston, New York Zbl0098.28301MR125252
2. A. Krazer, Lehrbuch der Theta - Funktionen, (1971), Chelsea, New York Zbl0212.42901

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