The function f(z) expanded in a Laurent series exhibits a pole of order mat z = z_0. Show that th...

The function f(z) expanded in a Laurent series exhibits a pole of order mat z = z_0. Show that the coefficient of (z - z_0)^-1, a_-1, is given by a_-1 = 1/(m - 1)! d^m-1/dz^m - 1 [(z - z_0)^m f(z)]_z = z_0, with a_-1 = [(z - z_0) f(z)]_z = z_0, when the pole is a simple pole (m = 1). These equations for a_-1 are extremely useful in determining the residue to be used in the residue theorem of the next section.