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.
In this paper, we study various arithmetic properties of the function p 2, k (n), which denotes the number of (2, k)-regular overpartitions of n with odd k > 1. We prove several infinite families of congruences modulo 8 for p 2, k (n). For example, we find that for all non-negative integers β, n and k ≡ 1 (mod 8),Mathematics Subject Classification 05A15 · 05A17 · 11P83
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