Gamma Function Using Spouge's Method

08252015, 06:48 PM
(This post was last modified: 08252015 09:43 PM by Dieter.)
Post: #28




RE: Gamma Function Using Spouge's Methjod
(08252015 01:56 AM)lcwright1964 Wrote: 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 All I know is that Mathematica and Maple (and most probably also others) offer some tools for rational and other approximations. But I do not have access to such software so I cannot say more about this. However... (08252015 01:56 AM)lcwright1964 Wrote: Or I could just stay with the original form, as you have, and fiddle with things in a spread sheet ...this approach has its special advantages. You can taylor an approximation exactly to meet your specific needs. For instance you may want to have better accuracy over a certain interval while for the rest a somewhat less accurate result will do. Or you may define a different error measure, for instance a max. number of ULPs the approximation can be off. That's what I like about the manual approach. Addendum: Les, you wanted an approxmation for n=5. I did some calculations on Free42 with 34digit BCD precision. The exact coefficients are not fixed yet, but with c=5.081 it looks like the relative error for x=0...70 is about ±4 E–13. Dieter 

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