Gamma Function Using Spouge's Method

[lcwright1964]

Hey Dieter,

This is excellent. I have learned that Free42 is an excellent place to observe the behaviour of HP41 programs. The programs are completely compatible without modification, 12-digits are displayed, and everything is done internally to 25 digits (not 34 like you say--that is DP mode in the WP34s). Indeed, working with JMB's GAM+ routine I have concluded there is likely little benefit to adding a term to the Stirling series. With ample available precision on Free42 GAM+ unedited computes the Gamma of 5.000000001, just a tad about the shift-divide cutoff, to about 10.4 edd. A further term can't improve on this on the HP41--indeed, even more computations will add to rounding error. And there is little to be gained by lowering the shift-divide cutoff, as adding a term likely adds more operations than what might be saved by lowering the cutoff.

For your Lanczos formula your reciprocals start at 1/z+1 instead of 1/z in my versions. Does this permit you to make sure the error curve passes through z = 0?

Les