A new approach to the derivation of exact analytical formulae for the zeros of sectionally analytic functions (Q1073204)

A new method for the analytical determination of zeros of sectionally analytic functions in the cut complex plane (or of poles of sectionally meromorphic functions), based only on the first Plemelj formula, is proposed. This method, like the analogous earlier methods of Burniston and Siewert and of the senior author, leads to the determination of these zeros (or poles) as the roots of a polynomial. The coefficients of this polynomial contain regular integrals along the discontinuity interval, which can be computed by appropriate (usually Gaußian) quadrature rules. The advantage of the present approach over the existing ones is its simplicity as a concept and ease during the application to particular sectionally analytic (or meromorphic) functions.