Charlier polynomials
Encyclopedia
In mathematics, Charlier polynomials (also called Poisson–Charlier polynomials) are a family of orthogonal polynomials
introduced by Carl Charlier
.
They are given in terms of the generalized hypergeometric function by
where
are Laguerre polynomials
. They satisfy the orthogonality
relation
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 polynomials, the Chebyshev polynomials, and the...
introduced by Carl Charlier
Carl Charlier
Carl Vilhelm Ludwig Charlier was a Swedish astronomer.He received his Ph.D. from Uppsala University in 1887, later worked there and at the Stockholm Observatory and was Professor of Astronomy and Director of the Observatory at Lund University from 1897.He made extensive statistical studies of the...
.
They are given in terms of the generalized hypergeometric function by
where
are Laguerre polynomialsLaguerre polynomials
In mathematics, the Laguerre polynomials, named after Edmond Laguerre ,are the canonical solutions of Laguerre's equation:x\,y + \,y' + n\,y = 0\,which is a second-order linear differential equation....
. They satisfy the orthogonality
relation