#
octave_polynomial

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

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Related Data and codes:

bernstein_polynomial,
an Octave code which
evaluates the Bernstein polynomials,
useful for uniform approximation of functions;

change_polynomial,
an Octave code which
uses a polynomial multiplication algorithm to count the ways of making
various sums using a given number of coins.

chebyshev_polynomial,
an Octave 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.

collatz_polynomial,
an Octave code which
implements the Collatz polynomial iteration, a polynomial analog of
the numerical iteration that is also known as the 3n+1 conjecture or
the hailstone sequence.

gegenbauer_polynomial,
an Octave code which
evaluates the Gegenbauer polynomial and associated functions.

gram_polynomial,
an Octave code which
evaluates the Gram polynomials, also known as the discrete Chebyshev
polyomials, and associated functions.

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

hermite_product_polynomial,
an Octave code which
defines Hermite product polynomials, creating a multivariate
polynomial as the product of univariate Hermite polynomials.

jacobi_polynomial,
an Octave code which
evaluates the Jacobi polynomial and associated functions.

laguerre_polynomial,
an Octave code which
evaluates the Laguerre polynomial, the generalized Laguerre polynomial,
and the Laguerre function.

legendre_polynomial,
an Octave code which
evaluates the Legendre polynomial and associated functions.

legendre_product_polynomial,
an Octave code which
defines Legendre product polynomials, creating a multivariate
polynomial as the product of univariate Legendre polynomials.

legendre_shifted_polynomial,
an Octave code which
evaluates the shifted Legendre polynomial, with domain [0,1].

lobatto_polynomial,
an Octave code which
evaluates Lobatto polynomials, similar to legendre polynomials
except that they are zero at both endpoints.

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Last revised on 18 December 2022.
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