O15-C079

> restart;
> f:=1+2*sum(r^n*cos(n*theta),n=1..infinity);

                             2 r (r - cos(theta))
                  f := 1 - ------------------------
                                                  2
                           -2 r cos(theta) + 1 + r

> 
> simplify(diff(f,r,r)+diff(f,r)/r+diff(f,theta,theta)/r^2);

                                  0

> g:=int(h(t)*subs(theta=theta-t,f),t=0..2*Pi)/2/Pi;

           /        2 Pi                                           \
           |       /                                               |
           | 1    |           /      2 r (r - cos(theta - t))  \   |
  g := 1/2 |----  |      h(t) |1 - ----------------------------| dt|
           | Pi   |           |                               2|   |
           |     /            \    -2 r cos(theta - t) + 1 + r /   |
           \       0                                               /

>