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We summarise the results of [6,7] and how they correspond to
the case **p=3**. Define
Then
We also mention the identity
This equation was known to Ramanujan [3, p. 199,].
See [2] for a proof using theta-functions.
We have

As usual we let
Then, from (6.9)--(6.12) we have
and
Now, from (6.7), (6.13), (6.14) we have
and, by (3.18), (6.16) we have
where
From (3.19), (3.20) we know that
and so
By letting,
we have the following
### Theorem 6.1

(Borwein and Borwein [6, Iteration 3.2, p. 699,])
Define sequences , , and by
Then converges cubically to .

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