Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ORTHOGONAL POLYNOMIALS SATISFYING PARTIAL DIFFERENTIAL EQUATIONS BELONGING TO THE BASIC CLASS

  • Lee, J.K. (Department of Mathematics SunMoon University) ;
  • L.L. Littlejohn (Department of Mathematics and Statistics Utah State University) ;
  • Yoo, B.H. (Department of Mathematics Education Andong University)
  • Published : 2004.11.01
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Abstract

We classify all partial differential equations with polynomial coefficients in $\chi$ and y of the form A($\chi$) $u_{{\chi}{\chi}}$ ＋ 2B($\chi$, y) $u_{{\chi}y}$ ＋ C(y) $u_{yy}$ ＋ D($\chi$) $u_{{\chi}}$ ＋ E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.

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References

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