A new approach to the derivation of exact integral formulae for zeros of analytic functions

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Ioakimidis, Nikolaos
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A new method for the reduction of the problem of locating the zeros of an analytic function inside a simple closed contour to that of locating the zeros of a polynomial is proposed. The new method (exactly like the presently used classical relevant method) permits in this way the derivation of exact integral formulae for these zeros if they are no more than four. The present approach is based on the solution of a simple homogeneous Riemann–Hilbert boundary value problem. An application to a classical problem in physics concerning neutron moderation is also made and numerical results obtained by using the trapezoidal quadrature rule are presented.
Complex variables, Analytic functions, Argument principle, Transcendental functions, Zeros, Roots, Exact integral formulae, Closed contours, Riemann–Hilbert boundary value problem, Numerical integration, Trapezoidal quadrature rule, Neutron moderation