We present several new families of Rogers-Ramanujan type identities related to the moduli 18 and 24. A few of the identities were found by either Ramanujan, Slater, or Dyson, but most are believed to be new. For one of these families, we discuss possible connections with Lie algebras. We also present two families of related false theta function identities.
Abstract. This paper studies ordinary and general convergence of the RogersRamanujan continued fraction.Let the continued fraction expansion of any irrational number t ∈ (0, 1) be denoted by [0, e 1 (t), e 2 (t), · · · ] and let the i-th convergent of this continued fraction expansion be denoted bywhere φ = (It is shown that if y ∈ Y S , then the Rogers-Ramanujan continued fraction R(y) diverges at y. S is an uncountable set of measure zero. It is also shown that there is an uncountable set of points G ⊂ Y S such that if y ∈ G, then R(y) does not converge generally.It is further shown that R(y) does not converge generally for |y| > 1. However we show that R(y) does converge generally if y is a primitive 5m-th root of unity, for some m ∈ N. Combining this result with a theorem of I. Schur then gives that the continued fraction converges generally at all roots of unity.
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