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Expanding Legendre polynomials

  • Rafael Ferraro ORCID logo EMAIL logo
Published/Copyright: March 1, 2025

Abstract

The expansion of Legendre polynomials P ( cos θ ) in cosines of multiples of θ is obtained by comparing the 2 -pole solution of Laplace equation in complex coordinates with its usual form in spherical coordinates.

MSC 2020: 33C45; 41A58

Funding statement: This work was supported by Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and Universidad de Buenos Aires. The author is a member of Carrera del Investigador Científico (CONICET, Argentina).

References

[1] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 2007. Search in Google Scholar

[2] J. D. Jackson, Classical Electrodynamics, 3rd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1975. Search in Google Scholar

[3] N. N. Lebedev, Special Functions & Their Applications, Dover, New York, 2009. Search in Google Scholar

[4] G. Sansone, Orthogonal Functions, Dover, New York, 2012. Search in Google Scholar

Received: 2025-01-28
Revised: 2025-02-20
Accepted: 2025-02-23
Published Online: 2025-03-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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