There are close connections with the theory of orthogonal polynomials.

There are several conditions that single out the classical orthogonal polynomials from the others.

One can also consider orthogonal polynomials for some curve in the complex plane.

The term is also used to describe similar formulas for other orthogonal polynomials.

There are an enormous number of other formulas involving orthogonal polynomials in various ways.

The following table summarises the properties of the classical orthogonal polynomials.

One can see that the Hamburger moment problem is intimately related to orthogonal polynomials on the real line.

This integral expression for can be expressed in terms of the orthogonal polynomials and as follows.

The second type of matching polynomial has remarkable connections with orthogonal polynomials.

The modern theory of orthogonal polynomials is of a definite but limited scope.

The classical orthogonal polynomials correspond to the three families of weights:

Bochner characterized classical orthogonal polynomials in terms of their recurrence relations.

Orthogonal polynomials of one variable defined by a non-negative measure on the real line have the following properties.

Those restricted classes are exactly "classical orthogonal polynomials".

An alternative to fitting m data points by a power series in the subsidiary variable, z, is to use orthogonal polynomials.

See in particular the orthogonal polynomials.

Polynomial chaos expansions, which use orthogonal polynomials to approximate the response surface.

The most commonly used orthogonal polynomials are orthogonal for a measure with support in a real interval.

He is remembered for the Gegenbauer polynomials, a class of orthogonal polynomials.

Although the correlation can be reduced by using orthogonal polynomials, it is generally more informative to consider the fitted regression function as a whole.

Mourad Ismail later studied sieved orthogonal polynomials in a long series of papers.

For regression with high-order polynomials, the use of orthogonal polynomials is recommended.

His early work on orthogonal polynomials and harmonic functions was neglected for many years, until publicized by .

Sometimes the measure has finite support, in which case the family of orthogonal polynomials is finite, rather than an infinite sequence.

They include many of the other orthogonal polynomials in 1 variable as special or limiting cases, described in the Askey scheme.