Relations Between Ramanujan’s Cubic Continued Fraction and a Continued Fraction of Order 12 and its Evaluations

Belakavadi Radhakrishna Srivatsa Kumar; Harekala Chandrashekara Vidya

doi:10.5666/KMJ.2018.58.2.319

Article

Kyungpook Mathematical Journal 2018; 58(2): 319-332

Published online June 23, 2018

Relations Between Ramanujan’s Cubic Continued Fraction and a Continued Fraction of Order 12 and its Evaluations

Belakavadi Radhakrishna Srivatsa Kumar^*, and Harekala Chandrashekara Vidya

Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal-576 104, India, e-mail: sri_vatsabr@yahoo.com and vidyaashwath@gmail.com

Received: February 10, 2017; Accepted: March 29, 2018

Abstract

Go to

Abstract

In the present paper, we establish relationship between continued fraction U(−q) of order 12 and Ramanujan’s cubic continued fraction G(−q) and G(qⁿ) for n = 1, 2, 3, 5 and 7. Also we evaluate U(q) and U(−q) by using two parameters for Ramanujan’s theta-functions and their explicit values.

Keywords: Ramanujan cubic continued fraction, Theta functions