### On 2- and 4- Dissection of a Continued Fraction of Ramanujan

#### Abstract

In this paper we give 2- and 4-dissection of a continued fraction of Ramanujan and its reciprocal, by using Jacobi triple product identity.

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G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley, Reading, Mass. 1976.

G. E. Andrews, B. C. Berndt, Ramanujan's Lost Notebook. Part I, Springer, New York, 2005.

R. Antony, A Comprehensive Analysis on Dissections of Continued Fractions,American Journal of Computational and Applied Mathematics, 4(1)2014, 1-8.

B. C. Berndt, Ramanujan's notebooks, Part III, Springer-Verlag, New York, 1991.

N. A. Herbert, Certain Results on 3-Dissection of Ratio of Innite Products Journal of International Academy of Physical Sciences, 17(2)(2013), 155- 165.

M. D. Hirschhorn, On the expansion of Ramanujan's continued fraction, Ramanujan J., 2(1998) 521-527.

M. D. Hirschhorn, On the expansion of a continued fraction of Gordon, Ramanujan J., 5(2001) 369-375.

M. D. Hirschhorn and Roselin, On the 2-, 3-, 4- and 6-dissections of Ra-manujan's cubic continued fraction and its reciprocal, in Proc. Ramanujan Rediscovered, Bangalore, India, June 1-5, 2009, RMS Lecture Note Series, Vol. 14 (Ramanujan Mathematical Society, 2009), 125-138.

M. D. Hirschhorn, On the 2- and 4-dissections of Ramanujan's continued fraction and its reciprocal, Ramanujan J. 24(2011) 85-92.

M. D. Hirschhorn, On the 2- and 4-dissections of the Rogers-Ramanujan functions, Ramanujan J. 40(2)(2016), 227-235.

R. P. Lewis and Z.-G. Liu, A conjecture of Hirschhorn on the 4-dissection of Ramanujan's continued fraction, Ramanujan J. 4(2000), 347-352.

Bernard L. S. Lin, On the expansion of a continued fraction of order twelve, Int. J. Number Theory, 9(8)(2013), 2019-2031.

P. K. Rawat, Identities connected with Ramanujan's continued fraction, Palestine Journal of Mathematics, 8(1)(2019), 242-248.

B. Srivastava, On 2-dissection and 4-dissection of Ramanujan's cubic continued fraction and identities, Tamsui Oxford Journal of Mathematical Sciences 23(3)(2007), 305-315.

M.S. Surekha, On the modular relations and dissections for a continued fraction of order sixteen, Palestine Journal of Mathematics, 6(1)(2017), 119-132.

E. X. W. Xia and X. M. Yao, The 8-dissection of the Ramanujan Gollnitz-Gordon continued fraction by an iterative method, Int. J. Number Theory, 7(6)(2011), 1589-1593.

E. X. W. Xia and X. M. Yao, On 2- and 4-Dissection for some innite products, Rocky mountain journal of mathematics, 43(6)2013, 2033-2047.

E. X. W. Xia and X. M. Yao, 4-Dissection and 8-Dissection for some innite product, Rocky mountain journal of mathematics, 44(5) (2014), 1685-1696.

O. X. M. Yao and E. X. W. Xia, On the 4-dissections of certain innite products, Ramanujan J., 30(2013), 1-7.

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