The Hardy-Ramanujan-Rademacher Expansion for cm,m,(n)

The Hardy-Ramanujan-Rademacher Expansion for cm,m,(n)
Author(s):
Mahadevaswamy. B.S.
Keywords:
Q – binominal co-efficient, Frobenius partitions, analogous congrevence
Abstract
In this paper we obtain the Hardy – Ramanujan – Rademacher series for ck,h(n) on the lines of L.W.Kolitsch. The existence of such series for c1,k(n) ck,1(n)and 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 ck,h(n). Andrews has established the two congruences c1-2(5n + 3) C2-1 (5n + 3) O (mod 5). We whow that the analogous congruence c2,2(5n + 3) O (mod 5) is false for n = 2. We also study generalised Frobenius partitions with some restriction on its parts.
Article Details
Unique Paper ID: 157484 Publication Volume & Issue: Volume 9, Issue 7 Page(s): 287 - 296
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