Gamma Function by Stieltjes Continued Fraction

09132015, 02:06 AM
Post: #14




RE: Gamma Function by Stieltjes Continued Fraction
Hey, Dieter, for HP41 work with 10 digits I think I am sticking with the refinement mentioned above. Expressing the coefficient that is around 5 to a few more digits doesn't seem to confer extra benefit on the HP41, and indeed when I plot the error curve in an arbitrary precision environment I really see no big improvement at all.
I should play around with your four term versions, but I suspect that the advantages of them are lost in a 10 digit environment and, if anything, the extra computations due to the extra term produce their own round off issues. Of course more accuracy is desirable for 12digit calculators, but the point is more of an academic curiosity, since the newer HPs like the 42s and 35s compute the gamma (actually factorial) on allowable noninteger arguments just fine. Of course, all of these great refinements are good candidates for MCODE programming, but I think none of them can top some of the optimized Lanczos approximations we were discussing elsewhere. Getting rid of the shiftdivide step for smaller arguments really goes far to speeding things up across the board. Les 

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