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?

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?