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Let rk(n) and tk(n) denote the number of representations of n as a sum of k squares, and as a sum of k triangular numbers, respectively. We give a generalization of the result rk(8n + k) = cktk(n), which holds for 1 ≤ k ≤ 7, where ck is a constant that depends only on k. Two proofs are provided. One involves generating functions and the other is combinatorial.

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Abstract. The main purpose of this note is to state and prove, in a simple, unified manner, several 17-continued fraction expansions found in Ramanujan's "lost" notebook. This is related to some recent works of G. E. Andrews and M. D. Hirschhorn.

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Abstract. The main purpose of this note is to state and prove, in a simple, unified manner, several 17-continued fraction expansions found in Ramanujan's "lost" notebook. This is related to some recent works of G. E. Andrews and M. D. Hirschhorn.

In this paper, we establish several modular relations for the Rogers-Ramanujan type functions of order eleven which are analogous to Ramanujan's forty identities for RogersRamanujan functions. Furthermore, we give interesting partition-theoretic interpretation of some of the modular relations which are derived in this paper.