Gamma Function Using Spouge's Method

[Dieter]

(08-24-2015 09:23 AM)lcwright1964 Wrote:  If you can start by sending me your optimized version of, say, my n = 4 result, that would really be fun to play with in Mathematica, particularly if you can produce one with more digits based on what I have given above.

OK, this is what I got until now for the n=4. I think this should be close to the optimum. If evaluated exactly, the maximum relative error for x = 0...70 is 1,599 E–11. But also with 13 digits in MCode the result should be sufficiently close to this.

Here are two sets of coefficients with 16 resp. 12-13 digits:

Code:

      16 digits                         12-13 digits
---------------------------------------------------------
 c =  3,8306414                    c =  3,8306414
a0 =  3,298498349730427 E-2       a0 =  3,29849834973 E-2
a1 =  1,187103291606358           a1 =  1,187103291606
a2 = -1,062638608755227           a2 = -1,062638608755
a3 =  1,860986212445602 E-1       a3 =  1,86098621245 E-1
a4 = -2,629985803711166 E-3       a4 = -2,62998580380 E-3

Dieter