A note on some modular equations using Theta functions
Downloads
DOI:
https://doi.org/10.26637/mjm401/010Abstract
In this paper, we have given simple proof to the modular equations using theta function identities.
Keywords:
Theta functions, Modular equationsMathematics Subject Classification:
34G20- Pages: 79-83
- Date Published: 01-01-2016
- Vol. 4 No. 01 (2016): Malaya Journal of Matematik (MJM)
N. D. Baruah, Modular equations for Ramanujans cubic continued fraction. J. Math. Anal. Appl., 268(1), (2002), 244-255 . DOI: https://doi.org/10.1006/jmaa.2001.7823
N. D. Baruah, On some of Ramanujans Schläfli-type "mixed" modular equations. J. Number Theory, 100(2), (2003), 270-294 . DOI: https://doi.org/10.1016/S0022-314X(02)00127-0
N. D. Baruah and N. Saikia, Two parameters for Ramanujan's Theta-functions and their explicit values, Rocky mountain J. of Math. 37, (2007), 1747-1790. DOI: https://doi.org/10.1216/rmjm/1199649823
B. C. Berndt, Ramanujan's Notebooks, Part III, Springer-Verlag, New York, (1991). DOI: https://doi.org/10.1007/978-1-4612-0965-2
B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer-Verlag, New York, (1994). DOI: https://doi.org/10.1007/978-1-4612-0879-2
S. Bhargava, K. R. Vasuki and K. R. Rajanna, On Certain Identities of Ramanujan for Ratios of Eta Functions, Ukranian Mathematical Journal, 66(8), (2015), 1131-1151. DOI: https://doi.org/10.1007/s11253-015-0999-y
S.-Y. Kang, Some Theorems in Rogers-Ramanujan Continued Fraction and Associated Theta Functions in Ramanujans 'Lost' Notebook, Ramanujan Journal, 3(1), (1999), 91-111. doi:10.1023/ A:1009869426750.
M. S. Mahadeva Naika, A note on cubic modular equations of degree two. Tamsui Oxf. J. Math. Sci., 22(1), (2006), 1-8 .
M. S. Mahadeva Naika, S. Chandan Kumar, Some new Schläfli-type modular equations in quartic theory. In: Ramanujan Math. Soc. Lect. Notes Ser., 14, 185-199. Ramanujan Math. Soc., Mysore (2010).
K. R. Vasuki, Sreeramamurthy, T.G. A note on PQ modular equations. Tamsui Oxf. J. Math. Sci., 21(2), (2005), 109-120 .
K. R. Vasuki, On some of Ramanujans P-Q modular equations. J. Indian Math. Soc., 73(3-4), 131-143 .
- NA
Similar Articles
- T.R. Ramesh Rao, A study on linear and non linear Schrodinger equations by reduced differential transform method , Malaya Journal of Matematik: Vol. 4 No. 01 (2016): 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) 2016 MJM
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.