Analytic proof of the partition identity A 5,3,3(n)=B 5,3,3 0 (n)

In this paper we give an analytic proof of the identity A _5,3,3(n)=B _5,3,3⁰(n), where A _5,3,3(n) counts the number of partitions of n subject to certain restrictions on their parts, and B _5,3,3⁰(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 Proceedings of the International Conference on Analytic Number Theory with Special Emphasis on L-functions, Ramanujan Math. Soc., Mysore, 2005, pp. 57–70], where it was also given a combinatorial proof, thus answering a question of Andrews. Research partially supported by EC’s IHRP Programme, grant HPRN-CT-2001-00272, “Algebraic Combinatorics in Europe.”