LAGUERRE_POLYNOMIAL, a C++ library 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.
BERNSTEIN_POLYNOMIAL, a C++ library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
CHEBYSHEV_POLYNOMIAL, a C++ library which evaluates the Chebyshev polynomial and associated functions.
GEGENBAUER_POLYNOMIAL, a C++ library which evaluates the Gegenbauer polynomial and associated functions.
GEN_LAGUERRE_RULE, a C++ program which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_POLYNOMIAL, a C++ library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
JACOBI_POLYNOMIAL, a C++ library which evaluates the Jacobi polynomial and associated functions.
LAGUERRE_RULE, a C++ program which can compute and print a Gauss-Laguerre quadrature rule.
LEGENDRE_POLYNOMIAL, a C++ library which evaluates the Legendre polynomial and associated functions.
LEGENDRE_SHIFTED_POLYNOMIAL, a C++ library which evaluates the shifted Legendre polynomial, with domain [0,1].
LOBATTO_POLYNOMIAL, a C++ library which evaluates Lobatto polynomials, similar to Legendre polynomials except that they are zero at both endpoints.
POLPAK, a C++ library which evaluates a variety of mathematical functions.
TEST_VALUES, a C++ library which supplies test values of various mathematical functions.