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

Charlier polynomials

In mathematics, Charlier polynomials are a family of orthogonal polynomials introduced by Carl Charlier....

, Krawtchouk polynomials, Meixner polynomials, dual Hahn polynomials, Hahn polynomials

Hahn polynomials

In mathematics, the Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials, introduced by Chebyshev in 1875 and rediscovered by . The Hahn class is a name for special cases of Hahn polynomials, including Hahn polynomials, Meixner...

, and Racah polynomials

Racah polynomials

In mathematics, Racah polynomials are orthogonal polynomials named after Giulio Racah, as their orthogonality relations are equivalent to his orthogonality relations for Racah coefficients....

.

If the measure has finite support, then the corresponding sequence of discrete orthogonal polynomials has only a finite number of elements. The Racah polynomials

Racah polynomials

In mathematics, Racah polynomials are orthogonal polynomials named after Giulio Racah, as their orthogonality relations are equivalent to his orthogonality relations for Racah coefficients....

give an example of this.