Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CLASSIFICATION OF CLASSICAL ORTHOGONAL POLYNOMIALS

  • Kwon, Kil-H. (Department of Mathematics KAIST ) ;
  • Lance L.Littlejohn (Department of Mathematics and Statistics Utah State University )
  • Published : 1997.11.01
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Abstract

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.

Keywords

References

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