Definition
- The Cauchy index was first defined for a pole s of the rational function r by Augustin Louis Cauchy in 1837 using one-sided limits as:
- A generalization over the compact interval is direct (when neither a nor b are poles of r(x)): it is the sum of the Cauchy indices of r for each s located in the interval. We usually denote it by .
- We can then generalize to intervals of type since the number of poles of r is a finite number (by taking the limit of the Cauchy index over for a and b going to infinity).
Read more about this topic: Cauchy Index
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