(a) Show that the function ex cos y is a solution to the two-dimensional Laplace equation.
(b) Show that its quadratic Taylor polynomial at x = y = 0 is harmonic.
(c) What about its degree 3 Taylor polynomial?
(d) Can you state a general theorem?
(e) Test your result by looking at the Taylor polynomials of the harmonic function log[x - l)2 + y2].