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A construction of real weight functions for certain orthogonal polynomials in two variables |
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| Authors: | J.K. Lee L.L. Littlejohn |
| Affiliation: | a Department of Mathematics, SunMoon University, Kalsan-Ri TangJeong-Myun Asan-Si ChoongNam, South Korea b Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA |
| Abstract: | H.L. Krall and I.M. Sheffer considered the problem of classifying certain second-order partial differential equations having an algebraically complete, weak orthogonal bivariate polynomial system of solutions. Two of the equations that they considered are (x2+y)uxx+2xyuxy+y2uyy+gxux+g(y−1)uy=λu, |
| Keywords: | Second-order partial differential equation Bivariate orthogonal polynomials Weak orthogonal polynomials Polynomial killers Weight functions |
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