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orthopolynom (version 1.0-2)

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

1.0-2

License

GPL (>= 2)

Maintainer

Frederick Novomestky

Last Published

October 18th, 2009

Functions in orthopolynom (1.0-2)

hermite.h.inner.products

Inner products of Hermite polynomials

gegenbauer.weight

Weight function for the Gegenbauer polynomial

jacobi.p.inner.products

Inner products of Jacobi polynomials

jacobi.g.weight

Weight function for the Jacobi polynomial

schebyshev.u.recurrences

Recurrence relations for shifted Chebyshev polynomials

jacobi.matrices

Create list of Jacobi matrices from monic recurrence parameters

spherical.weight

Weight function for the spherical polynomial

slegendre.weight

Weight function for the shifted Legendre polynomial

chebyshev.s.inner.products

Inner products of Chebyshev polynomials

jacobi.p.weight

Weight function for the Jacobi polynomial

chebyshev.u.weight

Weight function for the Chebyshev polynomial

polynomial.integrals

Create list of polynomial integrals

jacobi.g.polynomials

Create list of Jacobi polynomials

jacobi.p.polynomials

Create list of Jacobi polynomials

glaguerre.polynomials

Create list of generalized Laguerre polynomials

chebyshev.u.polynomials

Create list of Chebyshev polynomials

glaguerre.recurrences

Recurrence relations for generalized Laguerre polynomials

chebyshev.u.recurrences

Recurrence relations for Chebyshev polynomials

legendre.weight

Weight function for the Legendre polynomial

jacobi.g.inner.products

Inner products of Jacobi polynomials

ultraspherical.polynomials

Create list of ultraspherical polynomials

ghermite.h.polynomials

Create list of generalized Hermite polynomials

ghermite.h.recurrences

Recurrence relations for generalized Hermite polynomials

hermite.h.recurrences

Recurrence relations for Hermite polynomials

hermite.he.recurrences

Recurrence relations for Hermite polynomials

Calculate the value of Pochhammer's symbol

laguerre.inner.products

Inner products of Laguerre polynomials

hermite.he.inner.products

Inner products of Hermite polynomials

schebyshev.t.recurrences

Recurrence relations for shifted Chebyshev polynomials

orthogonal.polynomials

Create orthogonal polynomials

jacobi.p.recurrences

Recurrence relations for Jacobi polynomials

chebyshev.c.recurrences

Recurrence relations for Chebyshev polynomials

chebyshev.c.inner.products

Inner products of Chebyshev polynomials

chebyshev.c.polynomials

Create list of Chebyshev polynomials

schebyshev.u.polynomials

Create list of shifted Chebyshev polynomials

ghermite.h.inner.products

Inner products of generalized Hermite polynomials

chebyshev.s.recurrences

Recurrence relations for Chebyshev polynomials

monic.polynomials

Create list of monic orthogonal polynomials

chebyshev.t.polynomials

Create list of Chebyshev polynomials

chebyshev.s.polynomials

Create list of Chebyshev polynomials

gegenbauer.polynomials

Create list of Gegenbauer polynomials

ghermite.h.weight

Weight function for the generalized Hermite polynomial

chebyshev.c.weight

Weight function for the Chebyshev polynomial

gegenbauer.inner.products

Inner products of Gegenbauer polynomials

gegenbauer.recurrences

Recurrence relations for Gegenbauer polynomials

hermite.h.polynomials

Create list of Hermite polynomials

hermite.he.weight

Weight function for the Hermite polynomial

polynomial.roots

Create a list of polynomial roots

glaguerre.weight

Weight function for the generalized Laguerre polynomial

polynomial.values

Create vector of polynomial values

legendre.inner.products

Inner products of Legendre polynomials

slegendre.inner.products

Inner products of shifted Legendre polynomials

polynomial.coefficients

Create list of polynomial coefficient vectors

spherical.polynomials

Create list of spherical polynomials

schebyshev.u.inner.products

Inner products of shifted Chebyshev polynomials

slegendre.polynomials

Create list of shifted Legendre polynomials

chebyshev.t.inner.products

Inner products of Chebyshev polynomials

legendre.polynomials

Create list of Legendre polynomials

chebyshev.s.weight

Weight function for the Chebyshev polynomial

polynomial.orders

Create vector of polynomial orders

monic.polynomial.recurrences

Create data frame of monic recurrences

hermite.h.weight

Weight function for the Hermite polynomial

chebyshev.t.weight

Weight function for the Chebyshev polynomial

glaguerre.inner.products

Inner products of generalized Laguerre polynomials

chebyshev.t.recurrences

Recurrence relations for Chebyshev polynomials

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

schebyshev.t.weight

Weight function for the shifted Chebyshev polynomial

polynomial.derivatives

Create list of polynomial derivatives

spherical.recurrences

Recurrence relations for spherical polynomials

chebyshev.u.inner.products

Inner products of Chebyshev polynomials

laguerre.weight

Weight function for the Laguerre polynomial

slegendre.recurrences

Recurrence relations for shifted Legendre polynomials

spherical.inner.products

Inner products of spherical polynomials

polynomial.powers

Create a list of polynomial linear combinations

ultraspherical.inner.products

Inner products of ultraspherical polynomials

schebyshev.t.polynomials

Create list of shifted Chebyshev polynomials

ultraspherical.weight

Weight function for the ultraspherical polynomial

hermite.he.polynomials

Create list of Hermite polynomials

jacobi.g.recurrences

Recurrence relations for Jacobi polynomials

laguerre.recurrences

Recurrence relations for Laguerre polynomials

laguerre.polynomials

Create list of Laguerre polynomials

Calculate the logarithm of Pochhammer's symbol

orthonormal.polynomials

Create orthonormal polynomials

legendre.recurrences

Recurrence relations for Legendre polynomials

schebyshev.u.weight

Weight function for the shifted Chebyshev polynomial

schebyshev.t.inner.products

Inner products of shifted Chebyshev polynomials

ultraspherical.recurrences

Recurrence relations for ultraspherical polynomials