lobatto_polynomial

lobatto_polynomial, an Octave 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) )
      

The completed Lobatto polynomial Lo(n,x) has degree n+1, and is zero at x = -1 and x = +1.

Licensing:

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

Languages:

lobatto_polynomial is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

lobatto_polynomial_test

octave_polynomial, an Octave code which analyzes a variety of polynomial families, returning the polynomial values, coefficients, derivatives, integrals, roots, or other information.

polpak, an Octave code which evaluates a variety of mathematical functions.

test_values, an Octave 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:

• lobatto_polynomial_derivative.m, returns the derivative of the completed Lobatto polynomials Lo'(n,x).
• lobatto_polynomial_plot.m, plots completed Lobatto polynomials Lo(n,x).
• lobatto_polynomial_value.m, returns the value of the completed Lobatto polynomials Lo(n,x).
• lobatto_polynomial_values.m, returns some tabulated values of the completed Lobatto polynomials Lo(n,x).