7 Feb 16:06 2008

### Re: numerical evaluation of psi0

Raymond Toy (RT/EUS <raymond.toy <at> ericsson.com>

2008-02-07 15:06:39 GMT

2008-02-07 15:06:39 GMT

Barton Willis wrote: > I evaluated psi[0](1.78095) using webMathematica, Maple 10, and Maxima > 5.14.0 to 50 > digits: > > Created by webMathematica > 0.27085244394958037219241274879122247322668078991599 > Maple > 0.27085617938915025987352993092362827661833339343790 > Maxima > 0.2708561793891502598735299309236282766183333934379b-1 > > (1) What's the story? You mean that Mma returns something different? I think you need to say 1.780950000<lots more zeroes>0. Something about how mma does some kind of significance arithmetic or something. I get something close to Maple's value then. > > (2) Does anybody have a reference to how our psi function works? It > seems to use a modified asymptotic expansion. I looked at bffac a while back that is the asymptotic series for log gamma. A peek at bfpsi shows that it is probably also the asymptotic series for psi. Probably A&S 6.3.18. (We should document these routines.) > > (3) Does our psi function work in the complex plane? --- you do need(Continue reading)