A q-CONTINUED FRACTION
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We use the method of generating functions to find the limit of a q-continued fraction, with 4 parameters, as a ratio of certain q-series. We then use this result to give new proofs of several known continued fraction identities, including Ramanujan's continued fraction expansions for (q2; q3)∞/(q; q3)∞and [Formula: see text]. In addition, we give a new proof of the famous Rogers–Ramanujan identities. We also use our main result to derive two generalizations of another continued fraction due to Ramanujan.
- Northwestern University United States
- West Chester University United States
- Trinity College Dublin Ireland
- Northern Illinois University United States
- Northeastern University United States
33D15, 11A55, 11B65, 30B70, \(q\)-continued fraction, Mathematics - Number Theory, Binomial coefficients; factorials; \(q\)-identities, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Continued fractions, Ramanujan, FOS: Mathematics, \(q\)-series, continued fractions, Number Theory (math.NT)
33D15, 11A55, 11B65, 30B70, \(q\)-continued fraction, Mathematics - Number Theory, Binomial coefficients; factorials; \(q\)-identities, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Continued fractions, Ramanujan, FOS: Mathematics, \(q\)-series, continued fractions, Number Theory (math.NT)
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