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arxiv: 1901.00584 · v1 · pith:DUAFZVMKnew · submitted 2019-01-03 · 🧮 math.NT

A q-continued fraction

classification 🧮 math.NT
keywords continuedfractioninftygiveidentitiesramanujanresultaddition
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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 $(q^2;q^3)_{\infty}/(q;q^3)_{\infty}$ and $(q;q^2)_\infty / (q^{3};q^{6})_\infty^3$. 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.

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