Gamma Function Using Spouge's Method

08252015, 11:29 PM
Post: #29




RE: Gamma Function Using Spouge's Methjod
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, 12digits are displayed, and everything is done internally to 25 digits (not 34 like you saythat 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 shiftdivide cutoff, to about 10.4 edd. A further term can't improve on this on the HP41indeed, even more computations will add to rounding error. And there is little to be gained by lowering the shiftdivide 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 

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