# lobatto_polynomial

lobatto_polynomial, a MATLAB code 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.

### Languages:

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

### Related Data and Programs:

bernstein_polynomial, a MATLAB code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

chebyshev_polynomial, a MATLAB code 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 MATLAB code which evaluates the Gegenbauer polynomial and associated functions.

hermite_polynomial, a MATLAB code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.

jacobi_polynomial, a MATLAB code which evaluates the Jacobi polynomial and associated functions.

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

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

polpak, a MATLAB code which evaluates a variety of mathematical functions.

test_values, a MATLAB code which supplies test values of various mathematical functions.

### Reference:

1. Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0-486-61272-4,
LC: QA47.A34.
2. Larry Andrews,
Special Functions of Mathematics for Engineers,
Second Edition,
Oxford University Press, 1998,
ISBN: 0819426164,
LC: QA351.A75.
3. Daniel Zwillinger, editor,
CRC Standard Mathematical Tables and Formulae,
30th Edition,
CRC Press, 1996.

### Source Code:

Last revised on 16 February 2019.