Gamma Function diffrent results from Prime / Wolfram

03122018, 02:45 PM
Post: #1




Gamma Function diffrent results from Prime / Wolfram
I have found that Gamma(1/3,216) gives different answers between Prime / Other Cas systems.
Prime / Xcas gives aprox 1.78918142756e+92 Mathematica / Wolf Alpha gives aprox 8.94591*10^91  1.54948*10^92 I Maxima gives a similar result to mathematica / alpha https://www.wolframalpha.com/input/?i=Ga...3,+216%5D I have noticed that Prime is giving the Magnitude of the Complex answer were as the other cas systems are giving the Complex result. why is this? This has been puzzling me for the last few days any help will be appreciated 

03122018, 04:45 PM
(This post was last modified: 03122018 04:46 PM by Joe Horn.)
Post: #2




RE: Gamma Function diffrent results from Prime / Wolfram
When you say Gamma(1/3,216) do you really mean Gamma((1/3,216))? They are different (look at the parentheses). The first is Gamma with two real arguments (not sure what that means mathematically), and the second is Gamma with one complex argument, same as Gamma(1/3216*i).
Observations: In Home, Gamma with two real arguments returns a result. Anybody know what it means? The builtin Help system doesn't mention that Gamma allows more than one argument. It also says that only real arguments are allowed, but complex arguments don't cause an error. Hmmm. <0ΙΈ0> Joe 

03122018, 04:53 PM
Post: #3




RE: Gamma Function diffrent results from Prime / Wolfram
(03122018 04:45 PM)Joe Horn Wrote: When you say Gamma(1/3,216) do you really mean Gamma((1/3,216))? They are different (look at the parentheses). The first is Gamma with two real arguments (not sure what that means mathematically), and the second is Gamma with one complex argument, same as Gamma(1/3216*i). Afaik Gamma(x,y) is the incomplete gamma function but currently is not documented in the built in documentation if you Integrate(e^x^3,x,0,6) you will get an answer based on the incomplete gamma function in CAS mode 

03122018, 05:15 PM
(This post was last modified: 03122018 05:17 PM by parisse.)
Post: #4




RE: Gamma Function diffrent results from Prime / Wolfram
igamma(1/n,z) inside Xcas/Prime is the incomplete gamma function for z real>0, but not for z<0. The numerical value of igamma(1/n,z) is coherent with the numerical integral of exp(x^n) for n odd.


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