Abstract
We derive a new special case C(q) of a general continued fraction recorded by Ramanujan in his Lost Notebook. We give a representation of the continued fraction C(q) as a quotient of Dedekind eta-function and then use it to prove modular identities connecting C(q) with each of the continued fractions \(C(-q)\), \(C(q^{2})\), \(C(q^{3})\), \(C(q^{5})\), \(C(q^{7})\), \(C(q^{11})\), \(C(q^{13})\) and \(C(q^{17})\). We also prove general theorems for the explicit evaluation of the continued fraction C(q) by using Ramanujan’s class invariants.
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Acknowledgements
The first author (N. Saikia) is thankful to Council of Scientific and Industrial Research of India for partially supporting the research work under the Research Scheme No. 25(0241)/15/EMR-II [F. No. 25(5498)/15]. The authors also thank anonymous refree for his/her valuable suggestions and comments.
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Saikia, N., Boruah, C. Some results on a special case of a general continued fraction of Ramanujan. Ann Univ Ferrara 64, 165–183 (2018). https://doi.org/10.1007/s11565-017-0283-1
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DOI: https://doi.org/10.1007/s11565-017-0283-1