A generalization of the Siewert–Burniston method for the determination of zeros of analytic functions

DOI10.1063/1.526448zbMath0566.30004OpenAlexW1968368843MaRDI QIDQ3681082

E. G. Anastasselou, Nikolaos I. Ioakimidis

Publication date: 1984

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.526448

zbMATH Keywords

Riemann-Hilbert boundary value problemSiewert-Burniston method

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Related Items (12)

On the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane ⋮ On a modification of the Koenig theorem ⋮ A unified Riemann-Hilbert approach to the analytical determination of zeros of sectionally analytic functions ⋮ Tchebychef-like method for the simultaneous finding zeros of analytic functions ⋮ All the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox-Wright function: illustration for genome multiplicity in survival of irradiated cells ⋮ Higher-order iterative methods for approximating zeros of analytic functions ⋮ Generalized Ostrowski root-finding method ⋮ A Note on the Closed-Form Determination of Zeros and Poles of Generalized Analytic Functions ⋮ Determination of poles of sectionally meromorphic functions ⋮ On the simultaneous determination of zeros of analytic or sectionally analytic functions ⋮ Application of the generalized Siewert-Burniston method to locating zeros and poles of meromorphic functions ⋮ Bernstein, Pick, Poisson and related integral expressions for LambertW

Cites Work

• Exact analytical solutions of \(ze^z=a\)
• Closed-form solution of the equations of caustics about cracks in fracture mechanics
• A new method for obtaining exact analytical formulae for the roots of transcendental functions
• Solutions of the equation \(ze^z=a(z+b)\)
• On double zeros of x-tanh(ax+b)
• Exact Analytical Solutions of the Transcendental Equation $\alpha \sin \zeta = \zeta $
• On computing eigenvalues in radiative transfer
• Discrete spectrum basic to kinetic theory
• An exact analytical solution of Kepler's equation

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