Critical Index

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

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

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

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.