Question: how to use For loop inside Procedure. i'm trying ti integrate sigma__xx for even and odd function

restart;
F0:=proc(sigma__xx,N)
local  x,y,Fx,Fy,:
assume (w,real,w>0):assume (h,real,h>0):

for n from 0 by 2 to N do Fx:=integrate(sigma__xx*cos(w*Zeta*h),Zeta=0..infinity):
end do;
for n from 1 by 2 to N do Fx:=integrate(sigma__xx*sin(w*Zeta*h),Zeta=0..infinity):
end do;
return [Fx]:
end proc;

sigma__xx := -(sqrt(Zeta^2*h^2+h^2)^(-n+2)*cos(n*arctan(h, Zeta*h))*n^2+sqrt(Zeta^2*h^2+h^2)^(-n+2)*cos(n*arctan(h, Zeta*h))*n-2*sqrt(Zeta^2*h^2+h^2)^(-n+2)*cos(n*arctan(h, Zeta*h)))*Zeta^2*h^2/(Zeta^2*h^2+h^2)^2+(sqrt(Zeta^2*h^2+h^2)^(-n+2)*cos(n*arctan(h, Zeta*h))*n^2-3*sqrt(Zeta^2*h^2+h^2)^(-n+2)*cos(n*arctan(h, Zeta*h))*n;

F0(sigma__xx,N);

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