Remarks for Basic Appell Series

Abstract

Abstract. Let k be an imaginary quadratic field, H the complex upper half plane, and let τ ∈ k∩H, q = exp(πiτ ). And let n, t be positive integers) is an algebraic number [10]. As a generalization of this result, we find several infinite series and products giving algebraic numbers using Ramanujan's 1 ψ 1 summation. These are also related to Rogers-Ramanujan continued fractions.