On some continued fraction expansions for the ratios of the function ρ(a, b)

Somashekara, D. D. and Shalini, S. L. and Narasimha Murthy, K. (2013) On some continued fraction expansions for the ratios of the function ρ(a, b). Note di Matematica, 33 (2). pp. 35-42. ISSN 1123-2536

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Abstract

In his lost notebook, Ramanujan has defined the function ρ(a, b) by ρ(a, b) := 1 + 1 b X∞ n=0 (−1)n q n(n+1)/2 a n b −n (−aq)n , where |q| < 1, and (a; q)n = Qn−1 k=0 (1 − aqk ), n = 1, 2, 3, . . . , and has given a beautiful reciprocity theorem involving ρ(a, b). In this paper we obtain some continued fraction expansions for the ratios of ρ(a, b) with some of its contiguous functions. We also obtain some interesting special cases of our continued fraction expansions which are analogous to the continued fraction identities stated by Ramanujan.

Item Type:	Article
Subjects:	E Mathematical Science > Mathematics
Divisions:	Department of > Mathematics
Depositing User:	Arshiya Kousar Library Assistant
Date Deposited:	30 Oct 2019 11:15
Last Modified:	30 Oct 2019 11:15
URI:	http://eprints.uni-mysore.ac.in/id/eprint/9675

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