Positive infinity symbol mutates in a +/- infinity within integral (gamma function)

[massimo]

I'm playing with CAS.

I tried to calculate the gamma function using my own definition (not the internal one).

g(x):=int(e^(-t)*t^(x-1),t,0,+infinity)

The CAS convert the +infinity to a +/-infinity. When you try to calculate the function using an integer value you obtain the right result:

g(5) gives 24

When you try to calculate the gamma for a rational number or a decimal you obtain this symbolic result:

g(5+1/3) gives int(t^5*e^(-t)/(t^(1/3))²,t,0,+/-infinity)

You can note that +infinity mutates in +/-infinity.

Why?

[Helge Gabert]

Doesn't happen to me.

define in CAS

g(t):=int(x^(t-1)*exp(-x),x,0,inf)

g(5)=24 OK

g(5+1/3)=int((3*x^4*x*e(-x))/3*(x^1/3)^(-2),x,0,inf) Note: No change to +/-inf

approx(Ans)=40.1289... OK

[massimo]

(02-16-2014 08:03 PM)Helge Gabert Wrote:  Doesn't happen to me.

I have CAS in Exact mode.

[Helge Gabert]

So do I.

[massimo]

On my calc or emulator, the problem appears when you set the Simplify settings in CAS to Minimum.
If you set it to None or Maximum the behavior is as expected.

BTW I set it to None and tried to obtain the same "error" by hand but I have not obtained any success so far.

[massimo]

The expand function changes +infinity in -/+infinity:

expand(int(t^x*e^(-t),t,0,+infinity))

gives

int(t^x*e^(-t),t,0,+/-infinity)