Gamma Function by Stieltjes Continued Fraction

[lcwright1964]

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 12-digit 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 non-integer arguments just fine.

Of course, all of these great refinements are good candidates for M-CODE programming, but I think none of them can top some of the optimized Lanczos approximations we were discussing elsewhere. Getting rid of the shift-divide step for smaller arguments really goes far to speeding things up across the board.

Les