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Hoenders and Slump[7]
describe a method for determining number and multiplicities of zeros of a function
based on a numerical quadrature technique, but as they show in their Tables 4-5, this
technique is unstable. It seems unlikely to us that any numerical technique
could decisively solve this problem. Symbolic methods can come to our aid in
some instances. First, if
are rational functions in
must be zero. Hence
A piecewise holomorphic function defined by
consisting of finitely many holomorphic
An expression
Our algorithm is restricted to a finite interval
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