On the infinite products derived from theta series I

Abstract

Let k be an imaginary quadratic field, h the complex upper half plane, and let tau is an element of h boolean AND k, q = e(pi i tau). In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, q(1/8)/1 + -q/1+q + -q(2)/1+q(2) + center dot center dot center dot ([1]) is transcendental.