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orthopolynom (version 1.0-4)

Collection of functions for orthogonal and orthonormal polynomials

Description

A collection of functions to construct sets of orthogonal polynomials and their recurrence relations. Additional functions are provided to calculate the derivative, integral, value and roots of lists of polynomial objects.

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Version

Install

install.packages('orthopolynom')

Monthly Downloads

7,238

Version

1.0-4

License

GPL (>= 2)

Maintainer

Frederick Novomestky

Last Published

January 29th, 2013

Functions in orthopolynom (1.0-4)

chebyshev.u.recurrences

Recurrence relations for Chebyshev polynomials

hermite.h.inner.products

Inner products of Hermite polynomials

hermite.he.polynomials

Create list of Hermite polynomials

chebyshev.c.inner.products

Inner products of Chebyshev polynomials

jacobi.p.polynomials

Create list of Jacobi polynomials

chebyshev.t.polynomials

Create list of Chebyshev polynomials

chebyshev.s.recurrences

Recurrence relations for Chebyshev polynomials

polynomial.orders

Create vector of polynomial orders

gegenbauer.recurrences

Recurrence relations for Gegenbauer polynomials

hermite.h.recurrences

Recurrence relations for Hermite polynomials

schebyshev.u.weight

Weight function for the shifted Chebyshev polynomial

slegendre.weight

Weight function for the shifted Legendre polynomial

slegendre.inner.products

Inner products of shifted Legendre polynomials

schebyshev.t.polynomials

Create list of shifted Chebyshev polynomials

slegendre.recurrences

Recurrence relations for shifted Legendre polynomials

ghermite.h.weight

Weight function for the generalized Hermite polynomial

glaguerre.inner.products

Inner products of generalized Laguerre polynomials

hermite.h.polynomials

Create list of Hermite polynomials

hermite.he.inner.products

Inner products of Hermite polynomials

hermite.he.recurrences

Recurrence relations for Hermite polynomials

orthogonal.polynomials

Create orthogonal polynomials

polynomial.functions

Coerce polynomials to functions

laguerre.polynomials

Create list of Laguerre polynomials

schebyshev.t.recurrences

Recurrence relations for shifted Chebyshev polynomials

spherical.inner.products

Inner products of spherical polynomials

chebyshev.c.polynomials

Create list of Chebyshev polynomials

legendre.inner.products

Inner products of Legendre polynomials

glaguerre.polynomials

Create list of generalized Laguerre polynomials

monic.polynomial.recurrences

Create data frame of monic recurrences

jacobi.g.polynomials

Create list of Jacobi polynomials

hermite.he.weight

Weight function for the Hermite polynomial

jacobi.g.recurrences

Recurrence relations for Jacobi polynomials

chebyshev.t.recurrences

Recurrence relations for Chebyshev polynomials

schebyshev.t.inner.products

Inner products of shifted Chebyshev polynomials

jacobi.g.inner.products

Inner products of Jacobi polynomials

polynomial.integrals

Create list of polynomial integrals

polynomial.roots

Create a list of polynomial roots

glaguerre.weight

Weight function for the generalized Laguerre polynomial

Calculate the value of Pochhammer's symbol

gegenbauer.polynomials

Create list of Gegenbauer polynomials

spherical.recurrences

Recurrence relations for spherical polynomials

polynomial.powers

Create a list of polynomial linear combinations

ghermite.h.recurrences

Recurrence relations for generalized Hermite polynomials

schebyshev.u.polynomials

Create list of shifted Chebyshev polynomials

hermite.h.weight

Weight function for the Hermite polynomial

ultraspherical.recurrences

Recurrence relations for ultraspherical polynomials

jacobi.p.inner.products

Inner products of Jacobi polynomials

gegenbauer.inner.products

Inner products of Gegenbauer polynomials

schebyshev.u.recurrences

Recurrence relations for shifted Chebyshev polynomials

jacobi.matrices

Create list of Jacobi matrices from monic recurrence parameters

legendre.polynomials

Create list of Legendre polynomials

ultraspherical.inner.products

Inner products of ultraspherical polynomials

orthonormal.polynomials

Create orthonormal polynomials

ultraspherical.weight

Weight function for the ultraspherical polynomial

Calculate the logarithm of Pochhammer's symbol

polynomial.coefficients

Create list of polynomial coefficient vectors

chebyshev.t.weight

Weight function for the Chebyshev polynomial

chebyshev.s.inner.products

Inner products of Chebyshev polynomials

chebyshev.u.inner.products

Inner products of Chebyshev polynomials

jacobi.p.recurrences

Recurrence relations for Jacobi polynomials

slegendre.polynomials

Create list of shifted Legendre polynomials

monic.polynomials

Create list of monic orthogonal polynomials

legendre.recurrences

Recurrence relations for Legendre polynomials

chebyshev.c.recurrences

Recurrence relations for Chebyshev polynomials

chebyshev.s.weight

Weight function for the Chebyshev polynomial

laguerre.inner.products

Inner products of Laguerre polynomials

polynomial.values

Create vector of polynomial values

jacobi.g.weight

Weight function for the Jacobi polynomial

laguerre.recurrences

Recurrence relations for Laguerre polynomials

laguerre.weight

Weight function for the Laguerre polynomial

ultraspherical.polynomials

Create list of ultraspherical polynomials

spherical.polynomials

Create list of spherical polynomials

polynomial.derivatives

Create list of polynomial derivatives

gegenbauer.weight

Weight function for the Gegenbauer polynomial

legendre.weight

Weight function for the Legendre polynomial

spherical.weight

Weight function for the spherical polynomial

chebyshev.s.polynomials

Create list of Chebyshev polynomials

schebyshev.u.inner.products

Inner products of shifted Chebyshev polynomials

glaguerre.recurrences

Recurrence relations for generalized Laguerre polynomials

chebyshev.u.polynomials

Create list of Chebyshev polynomials

ghermite.h.polynomials

Create list of generalized Hermite polynomials

Scale values from [a,b] to [u.v]

chebyshev.c.weight

Weight function for the Chebyshev polynomial

jacobi.p.weight

Weight function for the Jacobi polynomial

chebyshev.t.inner.products

Inner products of Chebyshev polynomials

ghermite.h.inner.products

Inner products of generalized Hermite polynomials

chebyshev.u.weight

Weight function for the Chebyshev polynomial

schebyshev.t.weight

Weight function for the shifted Chebyshev polynomial