Gamma Function diffrent results from Prime / Wolfram

[c0manche]

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

[Joe Horn]

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(1/3-216*i).

Observations: In Home, Gamma with two real arguments returns a result. Anybody know what it means? The built-in 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.

[c0manche]

(03-12-2018 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(1/3-216*i).

Observations: In Home, Gamma with two real arguments returns a result. Anybody know what it means? The built-in 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.

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

[parisse]

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.