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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

 0<|z_1|<=|z_2|<=|z_3|<=...,

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

 |z_m|<|z_(m+1)|

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


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References

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. https://mathworld.wolfram.com/CriticalIndex.html

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