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We prove several new general theorems for the explicit evaluation of the Rogers–Ramanujan continued fraction $$R(q)$$ R ( q ) by parametrization of Ramanujan’s theta-functions and give examples. We also establish general theorems for the explicit evaluation of the parameter $$k:=R(q)R^2(q)$$ k : = R ( q ) R 2 ( q ) defined by Ramanujan in his notebook leading to the explicit evaluations of $$R(q)$$ R ( q ) .
Computational Methods and Function Theory – Springer Journals
Published: Oct 22, 2013
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