A Continued fraction of Ramanujan and some Ramanujan-Weber class invariants

Adiga, Chandrashekar and Nasser, Bulkhali Saeed Abdo and Simsek, Yilmaz and Srivastava, H. M. (2017) A Continued fraction of Ramanujan and some Ramanujan-Weber class invariants. Filomat, 31 (13). pp. 3975-3997. ISSN 2406-0933

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Abstract

On Page 36 of his “lost” notebook, Ramanujan recorded four q-series representations of the famous Rogers-Ramanujan continued fraction. In this paper, we establish two q-series representations of Ramanujan’s continued fraction found in his “lost” notebook. We also establish three equivalent integral representations and modular equations for a special case of this continued fraction. Furthermore, we derive continued-fraction representations for the Ramanujan-Weber class invariants 1n and Gn and establish formulas connecting 1n and Gn. We obtain relations between our continued fraction with the Ramanujan- G¨ollnitz-Gordon and amanujan’s cubic continued fractions. Finally, we find some algebraic numbers and transcendental numbers associated with a certain continued fraction A(q) which is related to Ramanujan’s continued fraction F(a; b; q); the Ramanujan-G¨ollnitz-Gordon continued fraction H(q) and the Dedekind eta function(s).

Item Type:	Article
Subjects:	E Mathematical Science > Mathematics
Divisions:	Department of > Mathematics
Depositing User:	C Swapna Library Assistant
Date Deposited:	26 Jun 2019 09:25
Last Modified:	15 Jul 2022 09:22
URI:	http://eprints.uni-mysore.ac.in/id/eprint/3883

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