Journal of the Ramanujan Mathematical Society

Padmavathamma ¹

Affiliations
1 Department of Post-Graduate Studies and Research in Mathematics, University of Mysore, Manasagangotri, Mysore 570 006, IN

Abstract

Let n be a positive integer and let a_m,m,(n) (m'≤ m) denote th em-coloured (say r₁,....,r_m) generalised Frobenius partitions of n in which there are no odd parts of some m' colours say r₁,....,r_m, in the top row and no even parts of r₁,....,r_m in the bottom row. in this paper we obtain the Hardy-Ramanujan-Rademacher expansion for a_m,m,(n).

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Padmavathamma ¹

Affiliations
1 Department of Post-Graduate Studies and Research in Mathematics, University of Mysore, Manasagangotri, Mysore-570 006, IN

Abstract

Let n be a positive integer and let cΦ_m,m,(n) denote the partition function which enumerates the generalised Frobenius partitions of n into parts with m colours and m' repetitions. In this paper we obtain the Hardy- Ramanujan-Rademacher expansion for cΦ_m,m,(n). This is a sequel to a recent work of L.W.Kolitsch[4] concerning the expansion for cΦ_1,m,(n) and cΦ_m,1,(n).

Keywords

Generalised Frobenius Partitions, Hardy-Ramanujan-Rademacher Series.

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