The function f is defined by 1 1 - exp(z)* f(z) Show that f has poles of order 1 at the points z = i2kπ for k = Z, and calculate the residues at these poles.

I'm trying to find an example of a function that has a pole of order 5 at z=2 and a residue of 13.

The cyclic rule is a sometimes useful identity that applies to the situation in which three variables; x, y, and z are related to one another by a function, z = z(x, y). The rule is: (az/ax)(ax/ay)(ay/əz) = -1 (cyclic rule) Show that the cyclic rule holds for. x² + 2y²+ (1/2)z = 12