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Residue (Complex Analysis)

The constant $a_{-1}$ in the Laurent Series

f(z)=\sum_{n=-\infty}^\infty a_n(z-z_0)^n

of $f(z)$ is called the residue of $f(z)$. The residue is a very important property of a complex function and appears in the amazing Residue Theorem of Contour Integration.

See also Contour Integration, Laurent Series, Residue Theorem


Arfken, G. ``Calculus of Residues.'' §7.2 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 400-421, 1985.

© 1996-9 Eric W. Weisstein