An algorithm which allows digits of a given number to be calculated without requiring the computation of earlier digits. The BBP formula for pi is the best-known such algorithm, but an algorithm also exists for e.
Plouffe (2022) gives a particularly simple digit-extraction algorithm for the decimal digits of by defining
(1)
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Then the th digit to the right of the decimal point of for is given by
(2)
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where is the integer part and is the fractional part. Similar formulas can be obtained using
(3)
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and
(4)
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where is an Euler number, which gives a base-9 (or binary) digit extraction formula (Plouffe 2022). Similar results can be also obtained for , , , , , and (Plouffe 2022).