A digit-extraction algorithm 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) proposes a formula for decimal digits of 
by defining
 |
(1)
|
A candidate for the 
th digit to the right of the decimal
point of 
for 
is
 |
(2)
|
where 
is the integer part and 
is the fractional part.
To certify the digit, an error bound must exclude crossing
a decimal truncation boundary. A small absolute error
alone does not guarantee this. Similar approximations can be obtained using
 |
(3)
|
and
 |
(4)
|
where 
is an Euler number (Plouffe 2022). Plouffe uses the
first approximation for octal (base
8) digits and the second for decimal
digits, subject to the same truncation-boundary requirement. Related limits
and formulas can also be obtained for 
(Plouffe 2022).
'th Decimal Digit or Binary of 
and 
." 29 Jan 2022.