restart:
Gamma(x)=Int(exp(-t)*t^(x-1),t=0..infinity);
Gamma(1/2)=Int(exp(-t)*t^(1/2-1),t=0..infinity);
Gamma(1/2)=Int(exp(-t)*t^(-1/2),t=0..infinity);
t:=u^2;
restart:
dt:=2*u*du;
restart:
Gamma(1/2)=2*Int(exp(-u^2),u=0..infinity);
Gamma(1/2)=2*Q;
Q:=Int(exp(-u^2),u=0..infinity);
Qx:=Int(exp(-x^2),x=0..infinity);
Qy:=Int(exp(-y^2),y=0..infinity);
Qxy:=Int(exp(-x^2),x=0..infinity)*Int(exp(-y^2),y=0..infinity);
Qxy:=Int(Int(exp(-x^2)*exp(-y^2),x=0..infinity),y=0..infinity);
Qxy:=Int(Int(exp(-x^2-y^2),x=0..infinity),y=0..infinity);
r:=sqrt(x^2+y^2);
restart:
dxdy:=r*dr*d*theta;
restart:
Qxy:=Int(Int(r*exp(-r^2),r=0..infinity),theta=0..Pi/2);
Qxy:=Int(int(r*exp(-r^2),r=0..infinity),theta=0..Pi/2);
Qxy:=int(int(r*exp(-r^2),r=0..infinity),theta=0..Pi/2);
Q:=sqrt(1/4*Pi);
restart:
Gamma(1/2):=2*Q;
Gamma(1/2):=2*1/2*sqrt(Pi); |
