laguerre_polynomial, a FORTRAN77 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.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
laguerre_polynomial is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.
bernstein_polynomial, a FORTRAN77 library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
CHEBYSHEV_POLYNOMIAL, a FORTRAN77 library which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x). Functions are provided to evaluate the polynomials, determine their zeros, produce their polynomial coefficients, produce related quadrature rules, project other functions onto these polynomial bases, and integrate double and triple products of the polynomials.
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LAGUERRE_EXACTNESS, a FORTRAN77 program which tests the polynomial exactness of Gauss-Laguerre quadrature rules for integration over [0,+oo) with density function exp(-x).
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POLPAK, a FORTRAN77 library which evaluates a variety of mathematical functions.
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