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orthopolynom (version 1.0-6.1)

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

4,497

Version

1.0-6.1

License

GPL (>= 2)

Maintainer

Frederick Novomestky

Last Published

October 3rd, 2022

Functions in orthopolynom (1.0-6.1)

chebyshev.s.polynomials

Create list of Chebyshev polynomials
chebyshev.c.weight

Weight function for the Chebyshev polynomial
chebyshev.c.polynomials

Create list of Chebyshev polynomials
chebyshev.t.weight

Weight function for the Chebyshev polynomial
gegenbauer.weight

Weight function for the Gegenbauer polynomial
chebyshev.u.recurrences

Recurrence relations for Chebyshev polynomials
chebyshev.u.polynomials

Create list of Chebyshev polynomials
chebyshev.u.weight

Weight function for the Chebyshev polynomial
chebyshev.t.recurrences

Recurrence relations for Chebyshev polynomials
chebyshev.u.inner.products

Inner products of Chebyshev polynomials
gegenbauer.inner.products

Inner products of Gegenbauer polynomials
gegenbauer.recurrences

Recurrence relations for Gegenbauer polynomials
gegenbauer.polynomials

Create list of Gegenbauer polynomials
glaguerre.polynomials

Create list of generalized Laguerre polynomials
ghermite.h.inner.products

Inner products of generalized Hermite polynomials
glaguerre.inner.products

Inner products of generalized Laguerre polynomials
hermite.h.inner.products

Inner products of Hermite polynomials
ghermite.h.polynomials

Create list of generalized Hermite polynomials
glaguerre.recurrences

Recurrence relations for generalized Laguerre polynomials
hermite.h.polynomials

Create list of Hermite polynomials
jacobi.g.inner.products

Inner products of Jacobi polynomials
hermite.h.recurrences

Recurrence relations for Hermite polynomials
glaguerre.weight

Weight function for the generalized Laguerre polynomial
hermite.h.weight

Weight function for the Hermite polynomial
ghermite.h.recurrences

Recurrence relations for generalized Hermite polynomials
ghermite.h.weight

Weight function for the generalized Hermite polynomial
jacobi.g.recurrences

Recurrence relations for Jacobi polynomials
jacobi.g.polynomials

Create list of Jacobi polynomials
jacobi.g.weight

Weight function for the Jacobi polynomial
hermite.he.inner.products

Inner products of Hermite polynomials
hermite.he.polynomials

Create list of Hermite polynomials
jacobi.p.inner.products

Inner products of Jacobi polynomials
jacobi.p.polynomials

Create list of Jacobi polynomials
jacobi.matrices

Create list of Jacobi matrices from monic recurrence parameters
jacobi.p.recurrences

Recurrence relations for Jacobi polynomials
jacobi.p.weight

Weight function for the Jacobi polynomial
legendre.recurrences

Recurrence relations for Legendre polynomials
legendre.polynomials

Create list of Legendre polynomials
hermite.he.recurrences

Recurrence relations for Hermite polynomials
hermite.he.weight

Weight function for the Hermite polynomial
laguerre.polynomials

Create list of Laguerre polynomials
polynomial.roots

Create a list of polynomial roots
monic.polynomials

Create list of monic orthogonal polynomials
polynomial.integrals

Create list of polynomial integrals
polynomial.orders

Create vector of polynomial orders
laguerre.recurrences

Recurrence relations for Laguerre polynomials
laguerre.inner.products

Inner products of Laguerre polynomials
orthogonal.polynomials

Create orthogonal polynomials
polynomial.powers

Create a list of polynomial linear combinations
legendre.inner.products

Inner products of Legendre polynomials
legendre.weight

Weight function for the Legendre polynomial
laguerre.weight

Weight function for the Laguerre polynomial
monic.polynomial.recurrences

Create data frame of monic recurrences
orthonormal.polynomials

Create orthonormal polynomials
schebyshev.u.inner.products

Inner products of shifted Chebyshev polynomials
pochhammer

Calculate the value of Pochhammer's symbol
slegendre.inner.products

Inner products of shifted Legendre polynomials
polynomial.values

Create vector of polynomial values
slegendre.recurrences

Recurrence relations for shifted Legendre polynomials
scaleX

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

Recurrence relations for shifted Chebyshev polynomials
slegendre.polynomials

Create list of shifted Legendre polynomials
ultraspherical.weight

Weight function for the ultraspherical polynomial
polynomial.derivatives

Create list of polynomial derivatives
lpochhammer

Calculate the logarithm of Pochhammer's symbol
polynomial.functions

Coerce polynomials to functions
schebyshev.u.weight

Weight function for the shifted Chebyshev polynomial
ultraspherical.recurrences

Recurrence relations for ultraspherical polynomials
polynomial.coefficients

Create list of polynomial coefficient vectors
schebyshev.u.recurrences

Recurrence relations for shifted Chebyshev polynomials
schebyshev.t.inner.products

Inner products of shifted Chebyshev polynomials
schebyshev.u.polynomials

Create list of shifted Chebyshev polynomials
spherical.recurrences

Recurrence relations for spherical polynomials
spherical.weight

Weight function for the spherical polynomial
schebyshev.t.polynomials

Create list of shifted Chebyshev polynomials
schebyshev.t.weight

Weight function for the shifted Chebyshev polynomial
spherical.polynomials

Create list of spherical polynomials
spherical.inner.products

Inner products of spherical polynomials
slegendre.weight

Weight function for the shifted Legendre polynomial
ultraspherical.polynomials

Create list of ultraspherical polynomials
ultraspherical.inner.products

Inner products of ultraspherical polynomials
chebyshev.c.recurrences

Recurrence relations for Chebyshev polynomials
chebyshev.s.inner.products

Inner products of Chebyshev polynomials
chebyshev.s.weight

Weight function for the Chebyshev polynomial
chebyshev.t.polynomials

Create list of Chebyshev polynomials
chebyshev.s.recurrences

Recurrence relations for Chebyshev polynomials
chebyshev.c.inner.products

Inner products of Chebyshev polynomials
chebyshev.t.inner.products

Inner products of Chebyshev polynomials