Representation of ck,h (q)

In this paper, we obtain the Hardy – Ramanujan – Rademacher series for ck,h(n) on the lines of L.W. Kolitsch. The existence of such series for c1,k(n) and ck,l(n) was asked for by Andrews and later obtained by Kolitsch. Finally we extend the results on q-binomial coefficients and q-series representation of Andrews to our function ck,h(n). Andrews has established the two congruences c1,2(5n+3)  c2,1 (5n+3)  O (mod 5). We show that the analogous congruence c2,2 (5n+3)  O (mod 5) is false for n = 2. We also study generalised Frobenius partitions with some restriction on its parts.