We present some new relations between a continued fraction U(q) of order 12 (established by M. S. M. Naika et al.) and U(q n) for n = 7, 9, 11, 13:
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N. D. Baruah, “Modular equations for Ramanujan’s cubic continued fraction,” J. Math. Anal. Appl., 268, 244–255 (2002).
N. D. Baruah and R. Barman, “Certain Theta-function identities and Ramanujan’s modular equations of degree 3,” Indian J. Math., 48, No. 1, 113–133 (2006).
B. C. Berndt, Ramanujan Notebooks. Pt. III, Springer, New York (1991).
B. C. Berndt, Ramanujan Notebooks. Pt. V, Springer, New York (1998).
H. H. Chan, “On Ramanujan’s cubic continued fraction,” Acta Arithm., 73, No. 4, 343–355 (1995).
H. H. Chan and S. S. Huang, “On the Ramanujan–Göllnitz–Gordan continued fraction,” Ramanujan J., 1., 75–90 (1997).
B. Cho, J. K. Koo, and Y. K. Park, “Arithmetic of the Ramanujan–Göllnitz–Gordan continued fraction,” J. Number Theory, 4, No. 129, 922–947 (2009).
H. Göllnitz, “Partition mit Differenzebedingungen,” J. Reine Angew. Math., 25, 154–190 (1967).
B. Gordon, “Some continued fractions of the Rogers–Ramanujan type,” Duke Math. J., 32, 741–748 (1965).
G. H. Hardy, Ramanujan, Chelsea, New York (1978).
M. S. M. Naika, B. N. Dharmendra, and K. Shivashankra, “A continued fraction of order twelve,” Centr. Eur. J. Math., DOI, 10.2478/s11533-008-0031-y.
S. Ramanujan, Notebooks, Tata Inst. Fundam. Research, Bombay (1957).
S. Ramanujan, The “Lost” Notebook and Other Unpublished Papers, Narosa, New Delhi (1988).
L. J. Rogers, “On a type of modular relation,” Proc. London Math. Soc., 19, 387–397 (1920).
K. R. Vasuki and P. S. Guruprasad, “On certain new modular relations for the Rogers–Ramanujan type functions of order twelve,” Proc. Jangjeon Math. Soc. (to appear).
K. R. Vasuki, G. Sharath, and K. R. Rajanna, “Two modular equations for squares of the cubic functions with applications,” Note Math. (to appear).
K. R. Vasuki and B. R. Srivatsa Kumar, “Certain identities for Ramanujan–Göllnitz–Gordan continued fraction,” J. Comput. Appl. Math., 187, 87–95 (2006).
K. R. Vasuki and B. R. Srivatsa Kumar, Two Identities for Ramanujan’s Cubic Continued Fraction, Preprint.
K. R. Vasuki and S. R. Swamy, “A new identity for the Rogers–Ramanujan continued fraction,” J. Appl. Math. Anal. Appl., 2, No. 1, 71–83 (2006).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 12, pp. 1609–1619, December, 2010.
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Vasuki, K.R., Kahtan, A.A.A., Sharath, G. et al. On a continued fraction of order 12. Ukr Math J 62, 1866–1878 (2011). https://doi.org/10.1007/s11253-011-0476-1
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DOI: https://doi.org/10.1007/s11253-011-0476-1