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http://dx.doi.org/10.4134/JKMS.2004.41.6.1049

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)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.6, 2004 , pp. 1049-1070 More about this Journal
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.
Keywords
orthogonal polynomials in two variables; partial differential equation in the basic class;
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Times Cited By Web Of Science : 4  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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