Some finite generalizations of Euler's pentagonal number theorem

Ji-Cai Liu

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 2, page 525-531
  • ISSN: 0011-4642

Abstract

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Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.

How to cite

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Liu, Ji-Cai. "Some finite generalizations of Euler's pentagonal number theorem." Czechoslovak Mathematical Journal 67.2 (2017): 525-531. <http://eudml.org/doc/288221>.

@article{Liu2017,
abstract = {Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.},
author = {Liu, Ji-Cai},
journal = {Czechoslovak Mathematical Journal},
keywords = {$q$-binomial coefficient; $q$-binomial theorem; pentagonal number theorem},
language = {eng},
number = {2},
pages = {525-531},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some finite generalizations of Euler's pentagonal number theorem},
url = {http://eudml.org/doc/288221},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Liu, Ji-Cai
TI - Some finite generalizations of Euler's pentagonal number theorem
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 2
SP - 525
EP - 531
AB - Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.
LA - eng
KW - $q$-binomial coefficient; $q$-binomial theorem; pentagonal number theorem
UR - http://eudml.org/doc/288221
ER -

References

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  3. Berkovich, A., Garvan, F. G., 10.1006/jcta.2002.3281, J. Comb. Theory, Ser. A 100 (2002), 61-93. (2002) Zbl1016.05003MR1932070DOI10.1006/jcta.2002.3281
  4. Bromwich, T. J., An Introduction to the Theory of Infinite Series, Chelsea Publishing Company, New York (1991). (1991) Zbl0901.40001
  5. Ekhad, S. B., Zeilberger, D., The number of solutions of X 2 = 0 in triangular matrices over GF( q ), Electron. J. Comb. 3 (1996), Research paper R2, 2 pages printed version in J. Comb. 3 1996 25-26. (1996) Zbl0851.15010MR1364064
  6. Petkovšek, M., Wilf, H. S., Zeilberger, D., A = B , With foreword by Donald E. Knuth, A. K. Peters, Wellesley (1996). (1996) Zbl0848.05002MR1379802
  7. Shanks, D., 10.1090/S0002-9939-1951-0043808-6, Proc. Am. Math. Soc. 2 (1951), 747-749. (1951) Zbl0044.28403MR0043808DOI10.1090/S0002-9939-1951-0043808-6
  8. Warnaar, S. O., 10.1007/s11139-005-0275-0, Ramanujan J. 8 (2004), 467-474. (2004) Zbl1066.05023MR2130521DOI10.1007/s11139-005-0275-0

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