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Integration of the products of associated Legendre functions in the problems of wave scattering by penetrable bodies of revolution

DOI 10.18127/j00338486-201910(15)-07

Keywords:

E.I. Semernya – Post-graduate Student, Moscow Institute of Physics and Technology (State University)
E-mail: poshisholina @gmail.com
S.P. Skobelev – Dr.Sc.(Phys.-Math.), Leading Research Scientist, PJSC «Radiofizika» (Moscow); Associate Professor, Moscow Institute of Physics and Technology (State University)
E-mail: s.p.skobelev@mail.ru


Indefinite integrals arising in the problems of wave scattering by penetrable bodies of revolution solved with use of the projection methods in a spherical coordinate system are considered. Explicit expressions for the integrals containing products of the associate Legendre functions of different degrees and identical orders   are derived. A recurrent relation for the integrals containing squares of the Legendre functions   are obtained, for which a recurrent relation corresponding to the case when the order of the function is equal to its degree is additionally derived. Some examples characterizing effectiveness of calculations with use of the derived expressions and relations are presented and discussed.

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May 29, 2020

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