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Positive infinity symbol mutates in a +/- infinity within integral (gamma function) - massimo - 02-16-2014 12:13 PM
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?
RE: Positive infinity symbol mutates in a +/- infinity within integral (gamma function) - Helge Gabert - 02-16-2014 08:03 PM
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
RE: Positive infinity symbol mutates in a +/- infinity within integral (gamma function) - massimo - 02-16-2014 09:43 PM
(02-16-2014 08:03 PM)Helge Gabert Wrote: Doesn't happen to me.
I have CAS in Exact mode.
RE: Positive infinity symbol mutates in a +/- infinity within integral (gamma function) - Helge Gabert - 02-17-2014 12:22 AM
So do I.
RE: Positive infinity symbol mutates in a +/- infinity within integral (gamma function) - massimo - 02-17-2014 06:28 AM
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.
RE: Positive infinity symbol mutates in a +/- infinity within integral (gamma function) - massimo - 02-17-2014 10:53 AM
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)