Gamma function

[ftneek]

With normalize(ex)) in g3, symbolic result is different:
g3(Gamma(x)) -> (x-1)!/ABS((x-1)!)

(08-16-2024 08:04 PM)Albert Chan Wrote:  Cas> Gamma2(a) := piecewise((len(a)==2 AND a[2]==0),Gamma(a[1]), (len(a)==2 AND a[2]==inf),0, Gamma(a))

I tried this updated Gamma2 method, it incorrectly applied Gamma(Gamma(x))
Gamma2(Gamma(x))
-> ((x-1)!-1)!

It should have just returned Gamma(x)=(x-1)!

fix is for the last piecewise statement:

Quote:Gamma2(a) := piecewise((len(a)==2 AND a[2]==0),Gamma(a[1]), (len(a)==2 AND a[2]==inf),0, a);
g3(ex) := ex (Gamma = Gamma2);

Gamma2(Gamma(x)) -> (x-1)!
g3(laplace(t^(-1/3),t,s) -> s^(1/3)*Gamma(2/3)/s

No need to normalize g3, and Gamma2 can handle symbolic gamma expression.

Edit: I may have misunderstood because of the optional argument. The arguments are Gamma2(a,[b]). Without b, Gamma(a) is expected. So Gamma(Gamma(x)) is correct, and my change to the last piecewise statement is not necessary (or correct).