LOBATTO_POLYNOMIAL, a C++ library which evaluates the completed Lobatto polynomial and associated functions.
The completed Lobatto polynomial Lo(n,x) can be defined by:
Lo(n,x) = n * ( P(n-1,x) - x * P(n,x) )where n is a positive integer called the order, x is a real value between -1 and +1, and P(n,x) is the Legendre polynomial.
The completed Lobatto polynomial Lo(n,x) has degree n+1, and is zero at x = -1 and x = +1.
GNUPLOT is used to create images of some of the functions.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
LOBATTO_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 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.
GEGENBAUER_POLYNOMIAL, a C++ library which evaluates the Gegenbauer polynomial and associated functions.
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_POLYNOMIAL, a C++ library which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.
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].
POLPAK, a C++ library which evaluates a variety of mathematical functions.
TEST_VALUES, a C++ library which supplies test values of various mathematical functions.