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) )
      
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.

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:


Last revised on 16 February 2019.