Gamma function

[Albert Chan]

(08-16-2024 06:06 PM)ftneek Wrote:  Is there an easy way to make the laplace example work using this method?

If I try your g3(laplace(t^(-1/3),t,s), I get this error:

"g3(laplace(t^((-1)/3),t,s)) in g3((-s*Gamma(2/3)+s*Gamma(2/3,0)+Gamma(2/3)*s-Gamma(2/3,∞)*s)/(s*(s^(1/3))^2)) instruction #1 error, try debug(g3((-s*Gamma(2/3)+s*Gamma(2/3,0)+Gamma(2/3)*s-Gamma(2/3,∞)*s)/(s*(s^(1/3))^2)))
Error: Bad Argument Value"

We can fix this 2 ways:
1. normal(ex) to g3, cancel out Gamma(x), before substitution.
2. fix Gamma2 to handle optional 2nd argument.

I think 2nd way to fix Gamma2 is better.
I applied 1st way too, just to show what I meant. (it may also be more efficient, with less substitutions)

Cas> Gamma2(a) := piecewise((len(a)==2 AND a[2]==0),Gamma(a[1]), (len(a)==2 AND a[2]==inf),0, Gamma(a))
Cas> g3(ex) := normal(ex) (Gamma = Gamma2)

Cas> g3(laplace(t^(-1/3),t,s)

s^(1/3)*Gamma(2/3)/s