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New Formulae for the Discrete Eigenvalues of the Homogeneous One-Speed Transport Equation

New closed-form formulae for the discrete eigenvalues of the classical homogeneous one-speed transport equation (in the case of plane symmetry), a fundamental equation in linear transport theory with a particular importance in neutron diffusion and transport with regeneration, are derived. A very simple method, based on the Cauchy theorem in the theory of analytic functions, is used for the derivation of these formulae. Finally, two more physical applications of the same formulae are reported.