Gamma Function Using Spouge's Method

[lcwright1964]

(08-24-2015 07:32 PM)Dieter Wrote:  Well, it's not magic. Just simple (really simple) math. ;-)

Eureka, I get it! You are basically applying some of the principles of the Remez algorithm in a manual way--i.e., you sample some points along the range in question, plot the error curve, and tweak things in the polynomial or rational approximation to smooth out the peaks and valleys. I haven't thought about this sort of stuff in ages. It frankly never occurred to me that one might take a certain rational or polynomial approximation and make it better this way. I always thought of this sort of minimax optimization as creating such formulae, not tweaking existing ones. Clever! Will try that myself.

And thank you for your kind words on my thoughts. I have taken some time off work this summer and the loss of structure has turned my sleep around, so I am up musing about this and other things at all odd hours.

Thanks for sharing your approach. I think I follow you very clearly, and it is most informative indeed.

Les