Abstract.In this paper we derive the power series expansions of four infinite products of the formwhere the index sets Si and S2 are specified with respect to a modulus (Theorems 1, 3, and 4). We also establish a useful formula for expanding the product of two Jacobi triple products (Theorem 2). Finally, we give nonexistence results for identities of two forms.
In this paper we derive the power series expansions of four infinite products of the form J](l-x") J](l + x"), nSSi neS2 where the index sets Si and S2 are specified with respect to a modulus (Theorems 1, 3, and 4). We also establish a useful formula for expanding the product of two Jacobi triple products (Theorem 2). Finally, we give nonexistence results for identities of two forms.
Abstract. Four new Ramanujan pairs {a,}, {6,} are given along with the theorem that no such pairs exist with at = 1 and a2 = s for any í > 5. All finite Ramanujan pairs are determined and their significance in bounding the local branching degree in the search tree for such pairs is discussed. The search techniques and programs that were used are also described. The parity of the coefficients in the power series is determined in two of the new identities. Partition interpretations of the six recent identities are also given.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.