Gamma Function Using Spouge's Method

[Dieter]

(08-24-2015 08:40 PM)lcwright1964 Wrote:  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.

Exactly. Usually I do these approximations even closer to the Remez method.

I now took another look at the n=4 coefficients, and guess what, it gets even better. I varied the c constant a bit and – for x=0...70 – the result did improve. With c=3,83 and 12-digit coefficients a relative error within ±2 E–11 is possible. That's 10,7 edd.

With 15-digit coefficients I just arrived at ±1,7 E–11. I wonder where we might get with an optimized set of all six coefficients, i.e. including c.

Dieter