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In this section we show how a computer algebra package like MAPLE
can be used to generate pth order iterations that converge
to from the functions .
For a fixed initial value and a fixed p
we define the sequence by
Of course, as it stands, although it is clear that
converges to to pth order, it is not very practical.
The idea is to write the sequence recursively. Therefore there are
two problems to solve:

Find initial values .

Get in terms of .
Table 1 contains some functions we defined in MAPLE and that we
used to find and prove initial values and iterations.
Table 1: MAPLE functions
Our function etaq utilizes the expansion due to Euler:
We are then able to effectively compute qseries expansions of , ,
. We have written MAPLE procedures to compute all the necessary
functions.
Contents
Next: Initial values
Up: Approximations to via the
Previous: The functions