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Polynomials

Table of contents

Generating functions

Betti number

Cyclic sieving

Factorial moment generating function

Generating function

Generating function transformation

Matsushima's formula

Moment-generating function

Probability-generating function

Tau function (integrable systems)

Weisner's method

Homogeneous polynomials

Quadratic forms

Complete homogeneous symmetric polynomial

Diagonal form

Elementary symmetric polynomial

Polynomial SOS

Power sum symmetric polynomial

SOS-convexity

Schur polynomial

Orthogonal polynomials

Affine q-Krawtchouk polynomials

Affine root system

Al-Salam–Carlitz polynomials

Al-Salam–Chihara polynomials

Askey scheme

Askey–Gasper inequality

Associated Legendre polynomials

Bateman polynomials

Bessel polynomials

Big q-Laguerre polynomials

Biorthogonal polynomial

Christoffel–Darboux formula

Classical orthogonal polynomials

Continuous Hahn polynomials

Continuous big q-Hermite polynomials

Continuous dual Hahn polynomials

Continuous dual q-Hahn polynomials

Continuous q-Hahn polynomials

Continuous q-Hermite polynomials

Continuous q-Jacobi polynomials

Continuous q-Laguerre polynomials

Discrete Chebyshev polynomials

Discrete orthogonal polynomials

Discrete q-Hermite polynomials

Dual Hahn polynomials

Dual q-Hahn polynomials

Favard's theorem

Gegenbauer polynomials

Hahn polynomials

Hall–Littlewood polynomials

Heckman–Opdam polynomials

Jack function

Jacobi polynomials

Koornwinder polynomials

Kravchuk polynomials

Little q-Jacobi polynomials

Little q-Laguerre polynomials

Macdonald polynomials

Mehler kernel

Mehler–Heine formula

Meixner polynomials

Meixner–Pollaczek polynomials

Multiple orthogonal polynomials

Orthogonal polynomials on the unit circle

Plancherel–Rotach asymptotics

Pseudo-Zernike polynomials

Pseudo Jacobi polynomials

Q-Bessel polynomials

Q-Charlier polynomials

Q-Hahn polynomials

Q-Krawtchouk polynomials

Q-Laguerre polynomials

Q-Meixner polynomials

Q-Meixner–Pollaczek polynomials

Q-Racah polynomials

Quantum q-Krawtchouk polynomials

Rodrigues' formula

Rogers polynomials

Sobolev orthogonal polynomials

Stieltjes–Wigert polynomials

Turán's inequalities

Zernike polynomials

Polynomial functions

Constant function

Cubic function

Linear function

Linear function (calculus)

Newton polytope

Quadratic function

Quartic function

Quintic function

Ring of polynomial functions

Polynomials factorization algorithms

Rational functions

Partial fractions

Chebyshev rational functions

Elliptic rational functions

Hartogs–Rosenthal theorem

Legendre rational functions

 Ancestors (4)

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