If a function f has a pole at z_0, then the negative power part sum_(j = - k)^(-1) a_j (z - z_0)^j of the Laurent series of f about z_0 sum_(j = - k)^∞ a_j (z - z_0)^j is called the principal part of f at z_0. For example, the principal part of (z^2 + 1)/(sin(z^3)) = z^(-3) + z^(-2) + 1/6 z^3 + 1/6 z^4 + ... is z^(-3) + z^(-2).

Laurent polynomial | Laurent series