Gamma Function Using Spouge's Method

08122015, 06:03 PM
Post: #5




RE: Gamma Function Using Spouge's Methjod
(08122015 05:39 PM)Dieter Wrote: So indeed the working precision has to be greater than the desired accuracy of the result. I assume that 13 digits would suffice for a 10 digit result. But this cannot be accomplished in a simple user program. On the '41, a 13digit MCode implementation would be possible. Indeed. I believe this is exactly what we have in Angel Martin's SANDMATH. Some years back I was quite engaged with approximating gamma. I learned that Lanczos and Spouge were attractive to some because they were convergent and as such one didn't get into the shift and divide thing for small arguments. Despite this, I think that programmers to this day go with the good oldfashioned Stirling's series, since in practice Spouge and Lanczos don't offer much more in the way of efficiency or accuracy. That said, I really can see that calculator programmers are drawn to the Spouge formula, as the coefficients are computed simply and on the fly. Nonetheless, JM Baillairds excellent GAM+ program in the old HP41 program archive here cleverly rearranges a truncated Stirling approximation in a way that maximizes efficiency and storage of coefficients. Les 

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