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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  9. Rogers, L. J., On the expansion of some infinite products, Proc. London Math. Soc. 24 (1893), 337–352. (1893) 
  10. Rogers, L. J., Second Memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318–343. (1894) 
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  13. Zhang, Z. Z., Liu, M. X., 10.1016/j.disc.2006.01.025, Discrete Math. 306 (2006), 1424–1437. (2006) Zbl1095.05002MR2237725DOI10.1016/j.disc.2006.01.025
  14. Zhang, Z. Z., Wang, J., 10.1016/j.jmaa.2005.03.064, J. Math. Anal. Appl. 312 (2) (2005), 653–665. (2005) Zbl1081.33032MR2179103DOI10.1016/j.jmaa.2005.03.064

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