Erich Kaltofen
and
C. Ryan Vinroot,
following their integer relation
approach (re)-discovered the following alternate formula:

A Maple V.4 session showing our derivation is here. This session can be loaded as Maple text and executed.

Adamchik and Wagon [Am. Math. Monthly, Nov. 1997;
url]
give the following pretty variant:

Their solution is dependent on the two given above as follows:

which is 2 times BBP plus 1 times our variant.

Fabrice Bellard has given a
formula
for base 2^{10}, which allows
a faster algorithm for computing the hexadecimal digits of .

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