lobatto_polynomial, a Python 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.


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


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

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  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 23 August 2023.