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  2. Legendre polynomials - Wikipedia

    en.wikipedia.org/wiki/Legendre_polynomials

    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. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections ...

  3. List of eponyms of special functions - Wikipedia

    en.wikipedia.org/wiki/List_of_eponyms_of_special...

    This is a list of special function eponyms in mathematics, ... Adrien-Marie Legendre: Legendre polynomials; Eugen Cornelius Joseph von Lommel (1837–1899), ...

  4. Legendre function - Wikipedia

    en.wikipedia.org/wiki/Legendre_function

    The general Legendre equation reads ″ ′ + [(+)] =, where the numbers λ and μ may be complex, and are called the degree and order of the relevant function, respectively. . The polynomial solutions when λ is an integer (denoted n), and μ = 0 are the Legendre polynomials P n; and when λ is an integer (denoted n), and μ = m is also an integer with | m | < n are the associated Legendre ...

  5. Associated Legendre polynomials - Wikipedia

    en.wikipedia.org/.../Associated_Legendre_polynomials

    In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation () + [(+)] =,or equivalently [() ()] + [(+)] =,where the indices ℓ and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively.

  6. Classical orthogonal polynomials - Wikipedia

    en.wikipedia.org/wiki/Classical_orthogonal...

    Classical orthogonal polynomials appeared in the early 19th century in the works of Adrien-Marie Legendre, who introduced the Legendre polynomials. In the late 19th century, the study of continued fractions to solve the moment problem by P. L. Chebyshev and then A.A. Markov and T.J. Stieltjes led to the general notion of orthogonal polynomials.

  7. List of things named after Adrien-Marie Legendre - Wikipedia

    en.wikipedia.org/wiki/List_of_things_named_after...

    Gauss–Legendre quadrature; Legendre (crater) Legendre chi function; Legendre duplication formula; Legendre–Papoulis filter; Legendre form; Legendre function; Legendre moment; Legendre polynomials; Legendre pseudospectral method; Legendre rational functions; Legendre relation; Legendre sieve; Legendre symbol; Legendre transformation ...

  8. List of polynomial topics - Wikipedia

    en.wikipedia.org/wiki/List_of_polynomial_topics

    Coefficient: An expression multiplying one of the monomials of the polynomial. Root (or zero) of a polynomial : Given a polynomial p ( x ), the x values that satisfy p ( x ) = 0 are called roots (or zeroes) of the polynomial p .

  9. Rodrigues' formula - Wikipedia

    en.wikipedia.org/wiki/Rodrigues'_formula

    The following proof shows that the polynomials obtained from the Rodrigues' formula obey the second order differential equation just given. This proof repeatedly uses the fact that the second derivative of B(x) and the first derivative of A(x) are constants.