laguerre_polynomial


laguerre_polynomial, a MATLAB code which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.

The Laguerre polynomial L(n,x) can be defined by:

        L(n,x) = exp(x)/n! * d^n/dx^n ( exp(-x) * x^n )
      
where n is a nonnegative integer.

The generalized Laguerre polynomial Lm(n,m,x) can be defined by:

        Lm(n,m,x) = exp(x)/(x^m*n!) * d^n/dx^n ( exp(-x) * x^(m+n) )
      
where n and m are nonnegative integers.

The Laguerre function can be defined by:

        Lf(n,alpha,x) = exp(x)/(x^alpha*n!) * d^n/dx^n ( exp(-x) * x^(alpha+n) )
      
where n is a nonnegative integer and -1.0 < alpha is a real number.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

laguerre_polynomial is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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gen_laguerre_rule, a MATLAB code which can compute and print a generalized gauss-laguerre quadrature rule.

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laguerre_polynomial_test

laguerre_rule, a MATLAB code which can compute and print a gauss-laguerre quadrature rule.

legendre_polynomial, a MATLAB code which evaluates the legendre polynomial and associated functions.

lobatto_polynomial, a MATLAB code which evaluates lobatto polynomials, similar to legendre polynomials except that they are zero at both endpoints.

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Reference:

  1. Theodore Chihara,
    An Introduction to Orthogonal Polynomials,
    Gordon and Breach, 1978,
    ISBN: 0677041500,
    LC: QA404.5 C44.
  2. Walter Gautschi,
    Orthogonal Polynomials: Computation and Approximation,
    Oxford, 2004,
    ISBN: 0-19-850672-4,
    LC: QA404.5 G3555.
  3. Frank Olver, Daniel Lozier, Ronald Boisvert, Charles Clark,
    NIST Handbook of Mathematical Functions,
    Cambridge University Press, 2010,
    ISBN: 978-0521192255,
    LC: QA331.N57.
  4. Gabor Szego,
    Orthogonal Polynomials,
    American Mathematical Society, 1992,
    ISBN: 0821810235,
    LC: QA3.A5.v23.

Source Code:


Last revised on 12 January 2021.