An excellent approximation of
FACT(N) was obtained by James Stirling in the 18 century. We use it in the following
STIRLING program for computing of the approximation of the factorial by the
Stirling's formula.
STIRLING: procedure
parse arg N, P
Pi = PI(P); E = E(P)
Sqrt2pin = SQRT(2 * Pi * N, P)
return,
Sqrt2pin * (N / E)**N * (1 + 1 / (12 * N))
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EXAMPLE
The FACT(10) computes the value 3628800 and STIRLING(10) computes the value 3628684.7
As N increases, the approximation to the factorial becomes more and more accurate.
FACT(108001) returns (in numeric digits 32 settings)
8.1428599075279953478037134061743E+496713 after 1.56 sec
STIRLING(108001,32) returns
8.1428599075255713876213611726275E+496713 after 0.02 sec
By the way, Calculator in Windows 2000 (PC 130MB RAM, 500MHz) displays 8.1428599075279953478037134061347E+496713 after (about) 900 seconds (15 minuts)
CONNECTIONS
