Bateman polynomials
Encyclopedia
In mathematics, the Bateman polynomials are a family Fn of orthogonal polynomials
introduced by . The Bateman–Pasternack polynomials are a generalization introduced by .
Bateman polynomials are given by
where Pn is a Legendre polynomial.
generalized the Bateman polynomials to polynomials F with
showed that the polynomials Qn studied by are the same as Bateman polynomials up to a change of variable: more precisely
Bateman and Pasternack's polynomials are special cases of the symmetric continuous Hahn polynomials
.
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 . The Bateman–Pasternack polynomials are a generalization introduced by .
Bateman polynomials are given by
where Pn is a Legendre polynomial.
generalized the Bateman polynomials to polynomials F with
showed that the polynomials Qn studied by are the same as Bateman polynomials up to a change of variable: more precisely
Bateman and Pasternack's polynomials are special cases of the symmetric continuous Hahn polynomials
Continuous Hahn polynomials
In mathematics, the continuous Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials...
.