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Gamma Function Using Spouge's Method
08-25-2015, 01:56 AM
Post: #27
RE: Gamma Function Using Spouge's Methjod
(08-24-2015 11:14 PM)Dieter Wrote:  Exactly. Usually I do these approximations even closer to the Remez method.

I have been looking at the MinimaxApproximation function in Mathematica which does this sort of thing. Alas, it seems to me it can only produce rational approximations in the strict sense--i.e. the numerator and denominator are each a polynomial in a certain argument.

With these Lanczos approximations, the series is in 1/z, 1/z+1, 1/z+2, etc., rather than just constant, z, z^2, z^3, etc. This is where Viktor Toth's rearrangement comes into play, to give

(z!/stuff in front)*Product(z+i, i=0..n) ~= polynomial in z of degree n

as the original approximation to be maximized.

Or I could just stay with the original form, as you have, and fiddle with things in a spread sheet Smile

Stuff to think about!

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RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-25-2015 01:56 AM

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