Gamma Function Using Spouge's Method
08-27-2015, 11:21 PM
Post: #33
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: Gamma Function Using Spouge's Methjod
(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
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 Messages In This Thread Gamma Function Using Spouge's Method - Namir - 12-18-2013, 12:55 AM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-07-2015, 07:23 PM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-12-2015, 04:03 AM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-12-2015, 05:39 PM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-12-2015, 06:03 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-12-2015, 09:11 PM RE: Gamma Function Using Spouge's Methjod - Ángel Martin - 08-19-2015, 08:56 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-20-2015, 11:36 AM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-20-2015, 07:49 PM RE: Gamma Function Using Spouge's Methjod - Ángel Martin - 08-21-2015, 09:48 AM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-22-2015, 02:09 AM RE: Gamma Function Using Spouge's Methjod - Ángel Martin - 08-22-2015, 08:35 AM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-22-2015, 08:58 AM RE: Gamma Function Using Spouge's Methjod - Ángel Martin - 08-22-2015, 10:45 AM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-19-2015, 05:32 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-20-2015, 12:36 PM RE: Gamma Function Using Spouge's Methjod - Thomas Klemm - 08-20-2015, 08:22 PM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-22-2015, 09:57 AM RE: Gamma Function Using Spouge's Methjod - Ángel Martin - 08-22-2015, 01:17 PM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-22-2015, 11:51 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-23-2015, 09:01 PM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-24-2015, 08:12 AM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-24-2015, 09:23 AM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-24-2015, 07:32 PM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-24-2015, 08:40 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-24-2015, 11:14 PM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-25-2015, 01:56 AM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-25-2015, 06:48 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-27-2015 11:21 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 09-15-2015, 06:43 PM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-25-2015, 11:29 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-26-2015, 09:50 AM RE: Gamma Function Using Spouge's Methjod - lcwright1964 - 08-26-2015, 12:50 PM RE: Gamma Function Using Spouge's Methjod - Dieter - 08-26-2015, 05:08 PM

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