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 |
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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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