Several q -series identities from the Euler expansions of ( a ; q ) ∞ and 1 ( a ; q ) ∞

Zhizheng Zhang; Yang, Jizhen

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 1, page 47-58
  • ISSN: 0044-8753

Abstract

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In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two q -series identities obtained by the Euler expansions of ( a ; q ) ∞ and 1 ( a ; q ) ∞ . Several q -series identities are obtained involving a q -series identity in Ramanujan’s Lost Notebook.

How to cite

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Zhang, Zhizheng, and Yang, Jizhen. "Several $q$-series identities from the Euler expansions of $(a;q)_{\infty }$ and $\frac{1}{(a;q)_{\infty }}$." Archivum Mathematicum 045.1 (2009): 47-58. <http://eudml.org/doc/250685>.

@article{Zhang2009,
abstract = {In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two $q$-series identities obtained by the Euler expansions of $(a;q)_\{\infty \}$ and $\frac\{1\}\{(a;q)_\{\infty \}\}$. Several $q$-series identities are obtained involving a $q$-series identity in Ramanujan’s Lost Notebook.},
author = {Zhang, Zhizheng, Yang, Jizhen},
journal = {Archivum Mathematicum},
keywords = {exponential operator; operator identity; $q$-series identity; exponential operator; operator identity; -series identity},
language = {eng},
number = {1},
pages = {47-58},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Several $q$-series identities from the Euler expansions of $(a;q)_\{\infty \}$ and $\frac\{1\}\{(a;q)_\{\infty \}\}$},
url = {http://eudml.org/doc/250685},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Zhang, Zhizheng
AU - Yang, Jizhen
TI - Several $q$-series identities from the Euler expansions of $(a;q)_{\infty }$ and $\frac{1}{(a;q)_{\infty }}$
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 1
SP - 47
EP - 58
AB - In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two $q$-series identities obtained by the Euler expansions of $(a;q)_{\infty }$ and $\frac{1}{(a;q)_{\infty }}$. Several $q$-series identities are obtained involving a $q$-series identity in Ramanujan’s Lost Notebook.
LA - eng
KW - exponential operator; operator identity; $q$-series identity; exponential operator; operator identity; -series identity
UR - http://eudml.org/doc/250685
ER -

References

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