The Cauchy Index
Preliminaries
- R(x) : a rational function q(x)/p(x), where p, q are polynomials.
- [a,b] : a closed interval, a < b. R does not become infinite at the end points.
Definition of the Cauchy index
By the Cauchy index, of R over [a,b], we mean
where denotes the number of points in (a,b) at which
R(x) jumps from , respectively, as x is
moving from a to b. Notice that from the definition.