On 3-Dissection Property
Downloads
DOI:
https://doi.org/10.26637/mjm202/004Abstract
The purpose of this paper is to derive 3- dissection for \(\left(q^2 ; q^2\right)_{\infty}^{-1}\left(q^4 ; q^4\right)_{\infty}^{-1}, \quad\left(q^3 ; q^3\right)_{\infty}^{-1}\left(q^6 ; q^6\right)_{\infty}^{-1}\) and \(\left(q^{\frac{1}{3}} ; q^{\frac{1}{3}}\right)_{\infty}^{-1}\left(q^{\frac{2}{3}} ; q^{\frac{2}{3}}\right)_{\infty}^{-1}\).
Keywords:
Partition functions, Generating functionsMathematics Subject Classification:
05A17, 05A15- Pages: 129-132
- Date Published: 01-04-2014
- Vol. 2 No. 02 (2014): Malaya Journal of Matematik (MJM)
H.-C.Chan, Ramanujan’s cubic continued fraction and a generalization of his most beautiful identity, Int. J. Number Theory, 6(2010), 673-680. DOI: https://doi.org/10.1142/S1793042110003150
H. Zhao and Z.Zhong, Ramanujan type congruences for a partition function,, The Electronic Journal of Combinatorics, 18(2011), 01-09. DOI: https://doi.org/10.37236/545
Z.Cao, On some dissection identities, J. Math. Anal. Appl., 365(2010), 659-667. DOI: https://doi.org/10.1016/j.jmaa.2009.11.038
J.M. Borwein, P.B. Borwein and F.G.Garvan, Some cubic modular identities of Ramanujan, Trans. Amer. Math.Soc., 343(1994),35-47. DOI: https://doi.org/10.1090/S0002-9947-1994-1243610-6
H.H. Chan and P.C. Toh, New analogues of Ramanujan’s partition identities, J. Number Theory, 130(2010), 1898-1913. DOI: https://doi.org/10.1016/j.jnt.2010.02.017
G.E.Andrews, R.Askey and R.Roy, Special Functions, Cambridge University Press, Cambridge, 1999. DOI: https://doi.org/10.1017/CBO9781107325937
B.C.Berndt, Number Theory in the Spirit of Ramanujan, Amer. Math. Soc., Providence, 2006. DOI: https://doi.org/10.1090/stml/034
- NA
Similar Articles
- Mehdi Nadjafikhah , Omid Chekini, Invariant solutions of Barlett and Whitaker’s equations , Malaya Journal of Matematik: Vol. 2 No. 02 (2014): Malaya Journal of Matematik (MJM)
- Mehdi Nadjafikhah, Omid Chekini, Classical and partial symmetries of the Benney equation , Malaya Journal of Matematik: Vol. 3 No. 01 (2015): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
