Orthogonal polynomials — In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the… … Wikipedia
Orthogonal polynomials on the unit circle — In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the complex plane, for some probability measure on the unit circle. They were introduced … Wikipedia
Classical orthogonal polynomials — In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical… … Wikipedia
Discrete orthogonal polynomials — In mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with repect to a discrete measure. Examples include the discrete Chebyshev polynomials, Charlier polynomials, Krawtchouk… … Wikipedia
Orthogonal functions — In mathematics, two functions f and g are called orthogonal if their inner product is zero for f ≠ g. Whether or not two particular functions are orthogonal depends on how their inner product has been defined. A typical definition of an … Wikipedia
Orthogonal wavelet — An orthogonal wavelet is a wavelet where the associated wavelet transform is orthogonal. That is the inverse wavelet transform is the adjoint of the wavelet transform. If this condition is weakened you may end up with biorthogonal wavelets.… … Wikipedia
Hermite polynomials — In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus; in numerical… … Wikipedia
Macdonald polynomials — In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal polynomials in several variables, introduced by Macdonald (1987). Macdonald originally associated his polynomials with weights λ of finite root systems and used just … Wikipedia
Chebyshev polynomials — Not to be confused with discrete Chebyshev polynomials. In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev,[1] are a sequence of orthogonal polynomials which are related to de Moivre s formula and which can be defined… … Wikipedia
Koornwinder polynomials — In mathematics, Koornwinder polynomials are a family of orthogonal polynomials in several variables, named for their discoverer Tom H. Koornwinder, that generalize the Askey Wilson polynomials. They can also be viewed as Macdonald polynomials… … Wikipedia
