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A new method for obtaining exact analytical formulae for the roots of transcendental functions

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Abstract

A new method is proposed for the derivation of closed-form formulae for the zeros and poles of sectionally analytic functions in the complex plane. This method makes use of the solution of the simple discontinuity problem in the theory of analytic functions and requires the evaluation of real integrals only (for functions with discontinuity intervals along the real axis). Many transcendental equations of mathematical physics can be successfully solved by the present approach. An application to such an equation, the molecular field equation in the theory of ferromagnetism, is made and the corresponding analytical formulae are reported together with numerical results.

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Authors and Affiliations

  1. Division of Applied Mechanics, The National Technical University of Athens, P.O. Box 61028, GR-151.10, Amaroussion, Greece

    E. G. Anastasselou

  2. Division of Applied Mathematics and Mechanics, School of Engineering, University of Patras, P.O. Box 1120, Gr-261.10, Patras, Greece

    N. I. Ioakimidis

Authors
  1. E. G. Anastasselou
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  2. N. I. Ioakimidis
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Anastasselou, E.G., Ioakimidis, N.I. A new method for obtaining exact analytical formulae for the roots of transcendental functions. Lett Math Phys 8, 135–143 (1984). https://doi.org/10.1007/BF00406396

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  • DOI: https://doi.org/10.1007/BF00406396

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