Analytic Proof of a Partition Identity 3 2 .

In this paper we give an analytic proof of the identity A 5,3,3 (n) = B 0 5,3,3 (n), where A 5,3,3 (n) counts the number of partitions of n subject to certain restrictions on their parts, and B 0 5,3,3 (n) counts the number of partitions of n subject to certain other restrictions on their parts, both too long to be stated in the abstract. Our proof establishes actually a refinement of that partition identity. The original identity was first discovered by the first author jointly with M. Ruby Salestina and S. R. Sudarshan in [ " A new theorem on partitions, " Proc. where it was also given a combinatorial proof, thus responding a question of Andrews.