Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PARTIAL DIFFERENTIAL EQUATIONS FOR PRODUCTS OF TWO CLASSICAL ORTHOGONAL POLYNOMIALS

  • LEE, D.W. (Department of Mathematics, Teachers College, Kyungpook National University)
  • Published : 2005.02.01
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Abstract

We give a method to derive partial differential equations for the product of any two classical orthogonal polynomials in one variable and thus find several new differential equations. We also explain with an example that our method can be extended to a more general case such as product of two sets of orthogonal functions.

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References

  1. S. Bochner, Uber Sturm-Liouvillesche Polynomsysteme, Math. Z. 29 (1929), 730-736 https://doi.org/10.1007/BF01180560
  2. T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1977
  3. T. H. Koornwinder, Two-variable analogues of the classical orthogonal polynomials, Theory and Applications of Special Functions, R. Askey Ed., Academic Press, 1975, 435-495
  4. H. L. Krall and I. M. Sheffer, Orthogonal polynomials in two variables, Ann. Mat. Pura Appl. 76 (1967), 325-376 https://doi.org/10.1007/BF02412238
  5. K. H. Kwon, D. W. Lee, and L. L. Littlejohn, Differential equations having orthogonal polynomial solutions, J. Comput. Appl. Math. 80 (1997), 1-16 https://doi.org/10.1016/S0377-0427(96)00096-9
  6. K. H. Kwon, Orthogonal polynomial eigenfunctions of second-order partial differential equations, Trans. Amer. Math. Soc. 353 (2001), 3629-3647 https://doi.org/10.1090/S0002-9947-01-02784-2
  7. K. H. Kwon and L. L. Littlejohn, Classification of classical orthogonal polynomials, J. Korean Math. Soc. 34 (1997), 973-1008
  8. L. L. Littlejohn, Orthogonal polynomial solutions to ordinary and partial differential equations, in Proc. 2nd International. Symp, Orthogonal Polynomials and their Applications, M. Alfaro et al. I(Eds), Lecture Notes Math. 1329, Springer, 1988, 98-124
  9. G. Szego, Orthogonal Polynomial, Amer. Math. Soc. Colloq. Publ. 23 (1975)

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