Legendre polynomials, named after Adrien-Marie Legendre who introduced them in 1782, are a system of complete and orthogonal polynomials with a wide range of mathematical properties and applications. They can be defined in several different ways, and the different definitions highlight different aspects of the polynomials as well as suggesting generalizations and connections to other mathematical structures and to physical and numerical applications. Several related families are closely tied to them, including the associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, and the big q-Legendre polynomials.
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Source Wikipedia: Legendre polynomials
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Source Wikipedia: Legendre polynomials
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1. Wikipedia: Legendre polynomials
Expanding an inverse distance potential
The Legendre polynomials were first introduced in 1782 by Adrien-Marie Legendre as the coefficients in the expansion of the Newtonian potential
Introduction
Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of mathematical properties and numerous applications.
In Branch: Analysis, Lead
In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of mathematical properties and numerous applications.
Attributed To: Adrien-Marie Legendre, Lead section
Legendre polynomials, named after Adrien-Marie Legendre (1782)
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