Critical Index

Let F be the Maclaurin series of a meromorphic function f with a finite or infinite number of poles at points z_k, indexed so that


then a pole will occur as many times in the sequence {z_k} as indicated by its order. Any index such that


holds is then called a critical index of f (Henrici 1988, pp. 641-642).

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Henrici, P. Applied and Computational Complex Analysis, Vol. 1: Power Series-Integration-Conformal Mapping-Location of Zeros. New York: Wiley, pp. 641-642, 1988.

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Critical Index

Cite this as:

Weisstein, Eric W. "Critical Index." From MathWorld--A Wolfram Web Resource.

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