Re: How to calculate factorial of fractions?

On Nov 10, 2:13 am, mike3 <mike4...@xxxxxxxxx> wrote:
On Nov 9, 7:18 pm, Sunil <sravip...@xxxxxxxxx> wrote:

I have seen several posts as to how to calculate factorial of
fractions like using gamma method. Can any one explain it using any
approximation such as sterling's?. I am able to calculate half
fractions using gamma but not the other fractions.

For example (3.142)!

You're right, you use the Gamma function:
3.142! = Gamma(4.142), exactly.

Stirling's series is an asymptotic series for the Gamma
function, which means that although it ultimately diverges,
it can be used to generate arbitrarily-good approximations
provided one makes the input to the function large enough.
Combined with the recurrence Gamma(z+1) = z*Gamma(z), one
can amplify the input to the size required for getting good
approximations.

See:

http://en.wikipedia.org/wiki/Asymptotic_expansion

Using the first few terms on that page even, we obtain
3.142! = Gamma(4.142) ~ 7.1918765295. The program I'm using
says the true value of Gamma(4.142) is closer to 7.1918772362,
so we'll just round the approximation from the asymptotic
to 7.191877. Not too bad, eh?

Look up the Lanczos Log Gamma approximation. Works in the whole
complex half plane with positive real part - use reflection formula
for negative real part.

.

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  • Re: How to calculate factorial of fractions?
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    (sci.math)
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