Orthogonal polynomials

Bateman polynomials

In mathematics, the Bateman polynomials are a family Fn of orthogonal polynomials introduced by Bateman. The Bateman–Pasternack polynomials are a generalization introduced by . Bateman polynomials can be defined by the relation where Pn is a Legendre polynomial. In terms of generalized hypergeometric functions, they are given by generalized the Bateman polynomials to polynomials Fmn with These generalized polynomials also have a representation in terms of generalized hypergeometric functions, namely showed that the polynomials Qn studied by , see Touchard polynomials, 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. (Wikipedia).

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From playlist Differential Equations

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From playlist Mathematics (All Of It)

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From playlist Mathematics

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From playlist Calculus

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From playlist Mathematics

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From playlist LatMath 2022 - IPAM's Latinx in the Mathematical Sciences Conference

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From playlist Differential Equations

Related pages

Continuous Hahn polynomials | Orthogonal polynomials | Generalized hypergeometric function | Touchard polynomials