orthopolynom: Collection of functions for orthogonal and orthonormal polynomials

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.

Author
Frederick Novomestky <fnovomes@poly.edu>
Date of publication
2013-02-04 07:42:24
Maintainer
Frederick Novomestky <fnovomes@poly.edu>
License
GPL (>= 2)
Version
1.0-5

View on CRAN

Man pages

chebyshev.c.inner.products
Inner products of Chebyshev polynomials
chebyshev.c.polynomials
Create list of Chebyshev polynomials
chebyshev.c.recurrences
Recurrence relations for Chebyshev polynomials
chebyshev.c.weight
Weight function for the Chebyshev polynomial
chebyshev.s.inner.products
Inner products of Chebyshev polynomials
chebyshev.s.polynomials
Create list of Chebyshev polynomials
chebyshev.s.recurrences
Recurrence relations for Chebyshev polynomials
chebyshev.s.weight
Weight function for the Chebyshev polynomial
chebyshev.t.inner.products
Inner products of Chebyshev polynomials
chebyshev.t.polynomials
Create list of Chebyshev polynomials
chebyshev.t.recurrences
Recurrence relations for Chebyshev polynomials
chebyshev.t.weight
Weight function for the Chebyshev polynomial
chebyshev.u.inner.products
Inner products of Chebyshev polynomials
chebyshev.u.polynomials
Create list of Chebyshev polynomials
chebyshev.u.recurrences
Recurrence relations for Chebyshev polynomials
chebyshev.u.weight
Weight function for the Chebyshev polynomial
gegenbauer.inner.products
Inner products of Gegenbauer polynomials
gegenbauer.polynomials
Create list of Gegenbauer polynomials
gegenbauer.recurrences
Recurrence relations for Gegenbauer polynomials
gegenbauer.weight
Weight function for the Gegenbauer polynomial
ghermite.h.inner.products
Inner products of generalized Hermite polynomials
ghermite.h.polynomials
Create list of generalized Hermite polynomials
ghermite.h.recurrences
Recurrence relations for generalized Hermite polynomials
ghermite.h.weight
Weight function for the generalized Hermite polynomial
glaguerre.inner.products
Inner products of generalized Laguerre polynomials
glaguerre.polynomials
Create list of generalized Laguerre polynomials
glaguerre.recurrences
Recurrence relations for generalized Laguerre polynomials
glaguerre.weight
Weight function for the generalized Laguerre polynomial
hermite.he.inner.products
Inner products of Hermite polynomials
hermite.he.polynomials
Create list of Hermite polynomials
hermite.he.recurrences
Recurrence relations for Hermite polynomials
hermite.he.weight
Weight function for the Hermite polynomial
hermite.h.inner.products
Inner products of Hermite polynomials
hermite.h.polynomials
Create list of Hermite polynomials
hermite.h.recurrences
Recurrence relations for Hermite polynomials
hermite.h.weight
Weight function for the Hermite polynomial
jacobi.g.inner.products
Inner products of Jacobi polynomials
jacobi.g.polynomials
Create list of Jacobi polynomials
jacobi.g.recurrences
Recurrence relations for Jacobi polynomials
jacobi.g.weight
Weight function for the Jacobi polynomial
jacobi.matrices
Create list of Jacobi matrices from monic recurrence...
jacobi.p.inner.products
Inner products of Jacobi polynomials
jacobi.p.polynomials
Create list of Jacobi polynomials
jacobi.p.recurrences
Recurrence relations for Jacobi polynomials
jacobi.p.weight
Weight function for the Jacobi polynomial
laguerre.inner.products
Inner products of Laguerre polynomials
laguerre.polynomials
Create list of Laguerre polynomials
laguerre.recurrences
Recurrence relations for Laguerre polynomials
laguerre.weight
Weight function for the Laguerre polynomial
legendre.inner.products
Inner products of Legendre polynomials
legendre.polynomials
Create list of Legendre polynomials
legendre.recurrences
Recurrence relations for Legendre polynomials
legendre.weight
Weight function for the Legendre polynomial
lpochhammer
Calculate the logarithm of Pochhammer's symbol
monic.polynomial.recurrences
Create data frame of monic recurrences
monic.polynomials
Create list of monic orthogonal polynomials
orthogonal.polynomials
Create orthogonal polynomials
orthonormal.polynomials
Create orthonormal polynomials
pochhammer
Calculate the value of Pochhammer's symbol
polynomial.coefficients
Create list of polynomial coefficient vectors
polynomial.derivatives
Create list of polynomial derivatives
polynomial.functions
Coerce polynomials to functions
polynomial.integrals
Create list of polynomial integrals
polynomial.orders
Create vector of polynomial orders
polynomial.powers
Create a list of polynomial linear combinations
polynomial.roots
Create a list of polynomial roots
polynomial.values
Create vector of polynomial values
scaleX
Scale values from [a,b] to [u.v]
schebyshev.t.inner.products
Inner products of shifted Chebyshev polynomials
schebyshev.t.polynomials
Create list of shifted Chebyshev polynomials
schebyshev.t.recurrences
Recurrence relations for shifted Chebyshev polynomials
schebyshev.t.weight
Weight function for the shifted Chebyshev polynomial
schebyshev.u.inner.products
Inner products of shifted Chebyshev polynomials
schebyshev.u.polynomials
Create list of shifted Chebyshev polynomials
schebyshev.u.recurrences
Recurrence relations for shifted Chebyshev polynomials
schebyshev.u.weight
Weight function for the shifted Chebyshev polynomial
slegendre.inner.products
Inner products of shifted Legendre polynomials
slegendre.polynomials
Create list of shifted Legendre polynomials
slegendre.recurrences
Recurrence relations for shifted Legendre polynomials
slegendre.weight
Weight function for the shifted Legendre polynomial
spherical.inner.products
Inner products of spherical polynomials
spherical.polynomials
Create list of spherical polynomials
spherical.recurrences
Recurrence relations for spherical polynomials
spherical.weight
Weight function for the spherical polynomial
ultraspherical.inner.products
Inner products of ultraspherical polynomials
ultraspherical.polynomials
Create list of ultraspherical polynomials
ultraspherical.recurrences
Recurrence relations for ultraspherical polynomials
ultraspherical.weight
Weight function for the ultraspherical polynomial

Files in this package

orthopolynom
orthopolynom/MD5
orthopolynom/R
orthopolynom/R/ultraspherical.weight.R
orthopolynom/R/ultraspherical.recurrences.R
orthopolynom/R/ultraspherical.polynomials.R
orthopolynom/R/ultraspherical.inner.products.R
orthopolynom/R/spherical.weight.R
orthopolynom/R/spherical.recurrences.R
orthopolynom/R/spherical.polynomials.R
orthopolynom/R/spherical.inner.products.R
orthopolynom/R/slegendre.weight.R
orthopolynom/R/slegendre.recurrences.R
orthopolynom/R/slegendre.polynomials.R
orthopolynom/R/slegendre.inner.products.R
orthopolynom/R/schebyshev.u.weight.R
orthopolynom/R/schebyshev.u.recurrences.R
orthopolynom/R/schebyshev.u.polynomials.R
orthopolynom/R/schebyshev.u.inner.products.R
orthopolynom/R/schebyshev.t.weight.R
orthopolynom/R/schebyshev.t.recurrences.R
orthopolynom/R/schebyshev.t.polynomials.R
orthopolynom/R/schebyshev.t.inner.products.R
orthopolynom/R/scaleX.R
orthopolynom/R/polynomial.values.R
orthopolynom/R/polynomial.roots.R
orthopolynom/R/polynomial.powers.R
orthopolynom/R/polynomial.orders.R
orthopolynom/R/polynomial.integrals.R
orthopolynom/R/polynomial.functions.R
orthopolynom/R/polynomial.derivatives.R
orthopolynom/R/polynomial.coefficients.R
orthopolynom/R/pochhammer.R
orthopolynom/R/orthonormal.polynomials.R
orthopolynom/R/orthogonal.polynomials.R
orthopolynom/R/monic.polynomials.R
orthopolynom/R/monic.polynomial.recurrences.R
orthopolynom/R/lpochhammer.R
orthopolynom/R/legendre.weight.R
orthopolynom/R/legendre.recurrences.R
orthopolynom/R/legendre.polynomials.R
orthopolynom/R/legendre.inner.products.R
orthopolynom/R/laguerre.weight.R
orthopolynom/R/laguerre.recurrences.R
orthopolynom/R/laguerre.polynomials.R
orthopolynom/R/laguerre.inner.products.R
orthopolynom/R/jacobi.p.weight.R
orthopolynom/R/jacobi.p.recurrences.R
orthopolynom/R/jacobi.p.polynomials.R
orthopolynom/R/jacobi.p.inner.products.R
orthopolynom/R/jacobi.matrices.R
orthopolynom/R/jacobi.g.weight.R
orthopolynom/R/jacobi.g.recurrences.R
orthopolynom/R/jacobi.g.polynomials.R
orthopolynom/R/jacobi.g.inner.products.R
orthopolynom/R/hermite.he.weight.R
orthopolynom/R/hermite.he.recurrences.R
orthopolynom/R/hermite.he.polynomials.R
orthopolynom/R/hermite.he.inner.products.R
orthopolynom/R/hermite.h.weight.R
orthopolynom/R/hermite.h.recurrences.R
orthopolynom/R/hermite.h.polynomials.R
orthopolynom/R/hermite.h.inner.products.R
orthopolynom/R/glaguerre.weight.R
orthopolynom/R/glaguerre.recurrences.R
orthopolynom/R/glaguerre.polynomials.R
orthopolynom/R/glaguerre.inner.products.R
orthopolynom/R/ghermite.h.weight.R
orthopolynom/R/ghermite.h.recurrences.R
orthopolynom/R/ghermite.h.polynomials.R
orthopolynom/R/ghermite.h.inner.products.R
orthopolynom/R/gegenbauer.weight.R
orthopolynom/R/gegenbauer.recurrences.R
orthopolynom/R/gegenbauer.polynomials.R
orthopolynom/R/gegenbauer.inner.products.R
orthopolynom/R/chebyshev.u.weight.R
orthopolynom/R/chebyshev.u.recurrences.R
orthopolynom/R/chebyshev.u.polynomials.R
orthopolynom/R/chebyshev.u.inner.products.R
orthopolynom/R/chebyshev.t.weight.R
orthopolynom/R/chebyshev.t.recurrences.R
orthopolynom/R/chebyshev.t.polynomials.R
orthopolynom/R/chebyshev.t.inner.products.R
orthopolynom/R/chebyshev.s.weight.R
orthopolynom/R/chebyshev.s.recurrences.R
orthopolynom/R/chebyshev.s.polynomials.R
orthopolynom/R/chebyshev.s.inner.products.R
orthopolynom/R/chebyshev.c.weight.R
orthopolynom/R/chebyshev.c.recurrences.R
orthopolynom/R/chebyshev.c.polynomials.R
orthopolynom/R/chebyshev.c.inner.products.R
orthopolynom/NAMESPACE
orthopolynom/man
orthopolynom/man/ultraspherical.weight.Rd
orthopolynom/man/ultraspherical.recurrences.Rd
orthopolynom/man/ultraspherical.polynomials.Rd
orthopolynom/man/ultraspherical.inner.products.Rd
orthopolynom/man/spherical.weight.Rd
orthopolynom/man/spherical.recurrences.Rd
orthopolynom/man/spherical.polynomials.Rd
orthopolynom/man/spherical.inner.products.Rd
orthopolynom/man/slegendre.weight.Rd
orthopolynom/man/slegendre.recurrences.Rd
orthopolynom/man/slegendre.polynomials.Rd
orthopolynom/man/slegendre.inner.products.Rd
orthopolynom/man/schebyshev.u.weight.Rd
orthopolynom/man/schebyshev.u.recurrences.Rd
orthopolynom/man/schebyshev.u.polynomials.Rd
orthopolynom/man/schebyshev.u.inner.products.Rd
orthopolynom/man/schebyshev.t.weight.Rd
orthopolynom/man/schebyshev.t.recurrences.Rd
orthopolynom/man/schebyshev.t.polynomials.Rd
orthopolynom/man/schebyshev.t.inner.products.Rd
orthopolynom/man/scaleX.Rd
orthopolynom/man/polynomial.values.Rd
orthopolynom/man/polynomial.roots.Rd
orthopolynom/man/polynomial.powers.Rd
orthopolynom/man/polynomial.orders.Rd
orthopolynom/man/polynomial.integrals.Rd
orthopolynom/man/polynomial.functions.Rd
orthopolynom/man/polynomial.derivatives.Rd
orthopolynom/man/polynomial.coefficients.Rd
orthopolynom/man/pochhammer.Rd
orthopolynom/man/orthonormal.polynomials.Rd
orthopolynom/man/orthogonal.polynomials.Rd
orthopolynom/man/monic.polynomials.Rd
orthopolynom/man/monic.polynomial.recurrences.Rd
orthopolynom/man/lpochhammer.Rd
orthopolynom/man/legendre.weight.Rd
orthopolynom/man/legendre.recurrences.Rd
orthopolynom/man/legendre.polynomials.Rd
orthopolynom/man/legendre.inner.products.Rd
orthopolynom/man/laguerre.weight.Rd
orthopolynom/man/laguerre.recurrences.Rd
orthopolynom/man/laguerre.polynomials.Rd
orthopolynom/man/laguerre.inner.products.Rd
orthopolynom/man/jacobi.p.weight.Rd
orthopolynom/man/jacobi.p.recurrences.Rd
orthopolynom/man/jacobi.p.polynomials.Rd
orthopolynom/man/jacobi.p.inner.products.Rd
orthopolynom/man/jacobi.matrices.Rd
orthopolynom/man/jacobi.g.weight.Rd
orthopolynom/man/jacobi.g.recurrences.Rd
orthopolynom/man/jacobi.g.polynomials.Rd
orthopolynom/man/jacobi.g.inner.products.Rd
orthopolynom/man/hermite.he.weight.Rd
orthopolynom/man/hermite.he.recurrences.Rd
orthopolynom/man/hermite.he.polynomials.Rd
orthopolynom/man/hermite.he.inner.products.Rd
orthopolynom/man/hermite.h.weight.Rd
orthopolynom/man/hermite.h.recurrences.Rd
orthopolynom/man/hermite.h.polynomials.Rd
orthopolynom/man/hermite.h.inner.products.Rd
orthopolynom/man/glaguerre.weight.Rd
orthopolynom/man/glaguerre.recurrences.Rd
orthopolynom/man/glaguerre.polynomials.Rd
orthopolynom/man/glaguerre.inner.products.Rd
orthopolynom/man/ghermite.h.weight.Rd
orthopolynom/man/ghermite.h.recurrences.Rd
orthopolynom/man/ghermite.h.polynomials.Rd
orthopolynom/man/ghermite.h.inner.products.Rd
orthopolynom/man/gegenbauer.weight.Rd
orthopolynom/man/gegenbauer.recurrences.Rd
orthopolynom/man/gegenbauer.polynomials.Rd
orthopolynom/man/gegenbauer.inner.products.Rd
orthopolynom/man/chebyshev.u.weight.Rd
orthopolynom/man/chebyshev.u.recurrences.Rd
orthopolynom/man/chebyshev.u.polynomials.Rd
orthopolynom/man/chebyshev.u.inner.products.Rd
orthopolynom/man/chebyshev.t.weight.Rd
orthopolynom/man/chebyshev.t.recurrences.Rd
orthopolynom/man/chebyshev.t.polynomials.Rd
orthopolynom/man/chebyshev.t.inner.products.Rd
orthopolynom/man/chebyshev.s.weight.Rd
orthopolynom/man/chebyshev.s.recurrences.Rd
orthopolynom/man/chebyshev.s.polynomials.Rd
orthopolynom/man/chebyshev.s.inner.products.Rd
orthopolynom/man/chebyshev.c.weight.Rd
orthopolynom/man/chebyshev.c.recurrences.Rd
orthopolynom/man/chebyshev.c.polynomials.Rd
orthopolynom/man/chebyshev.c.inner.products.Rd
orthopolynom/DESCRIPTION