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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 .

Contents
** Next:** The functions
**Up:** Approximations to via the
** Previous:** Introduction