(3) Stirling's formula is given by the following, depending on the accuracy you need:* In N! = N (ln N – 1) or, 1 In N! - N (In N – 1) +,In(2nN). Evaluate the accuracy of these formulas for N = 5, 10, 20, 60. Is it reasonable to expect the same accuracy for both formulas at very large N ? 2n *(Aside: Actual Stirling's formula is for gamma function r(z) = ,where z is a complex number, and r(n + 1) = n! for n E N.)
(3) Stirling's formula is given by the following, depending on the accuracy you need:* In N! = N (ln N – 1) or, 1 In N! - N (In N – 1) +,In(2nN). Evaluate the accuracy of these formulas for N = 5, 10, 20, 60. Is it reasonable to expect the same accuracy for both formulas at very large N ? 2n *(Aside: Actual Stirling's formula is for gamma function r(z) = ,where z is a complex number, and r(n + 1) = n! for n E N.)
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Transcribed Image Text:(3) Stirling's formula is given by the following, depending on the accuracy you need:*
In N! = N (ln N – 1)
or,
1
In N! - N (In N – 1) +,In(2tN).
Evaluate the accuracy of these formulas for N = 5,10, 20, 60. Is it reasonable to expect the same
accuracy for both formulas at very large N ?
*(Aside: Actual Stirling's formula is for gamma function r(z) =
, where z is a complex number, and r(n + 1) = n! for
пEN.)
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