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Solution of one class of systems of dual summation equations for associated Legendre functions

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We have obtained analytical solutions of one class of systems of dual summation equations for associated Legendre functions with fractional indices. Such equations appear in studying the interaction of vector electromagnetic fields with the circular edge of a conductive open cone in the low-frequency region. We have derived formulas for the reexpansion of Legendre functions, which are used for passage from summation equations to infinite systems of linear algebraic equations, containing convolution-type matrix operators. The operators inverse to them are applied for finding a solution in the required class of sequences. We give an example of determining the effect of interaction of TM- and TE-waves with the edge of a finite cone.

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Authors and Affiliations

  1. Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine

    D. B. Kuryliak

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  1. D. B. Kuryliak
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 1, pp. 48–58, January–March, 2009.

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Kuryliak, D.B. Solution of one class of systems of dual summation equations for associated Legendre functions. J Math Sci 168, 563–575 (2010). https://doi.org/10.1007/s10958-010-0007-x

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  • DOI: https://doi.org/10.1007/s10958-010-0007-x

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