Before we can define the alpha-function we need the following classical theta functions:


The alpha-function can be defined as


As r tends to infinity we see that q tends to zero so that we have


In [8, Theorem 3, p. 215,] Borwein, Borwein and Bailey are able to express in terms of and various theta functions. Utilizing p-th order modular equations for the theta functions, they then are able to construct p-th order iterations that converge to . In the next section we show how to construct p-th order iterations in a different way. Instead of a single alpha-function we construct an infinite family of functions .
Annotation Form Interface

          Your name: 
     E-Mail address: 
 Annotation Subject: 
        Related URL: