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Partial differential equations for products of two classical orthogonal polynomials

이동원
대한수학회 (The Korean Mathematical Society)|2005.02|대한수학회보 (Bulletin of the KMS)|제42권 제1호|pp. 179-188

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Abstract

We give a method to derive partial differential equations for theproduct of any two classical orthogonal polynomials in onevariable and thus find several new differential equations. We alsoexplain with an example that our method can be extended to a moregeneral case such as product of two sets of orthogonal functions.

참고문헌 (7)

  1. "An Introduction to Orthogonal Polynomials"
  2. "Two-variable analogues of the classical orthogonal polynomials Theory and Applications of Special Functions", pp.435~, Academic Press
  3. "Orthogonal polynomials in two variables", pp.325~ (1967)
  4. "Littlejohn, Differential equations having orthogonal polynomial solutions", 80, pp.1~16 (1997)
  5. "Orthogonal polynomial eigenfunctions of second-orderpartial differential equations", 353, pp.3629~3647 (2001)
  6. "Classification of classical orthogonal polynomials", 34, pp.973~1008 (1997)
  7. "Orthogonal polynomial solutions to ordinary and partial differentialequations", pp.98~ (1988)

관련 논문AI추천

Orthogonal polynomials satisfying partial differential equations belonging to the basic class유병훈, J. K. Lee, L. L. Littlejohn대한수학회 · 대한수학회지2004 · 제41권 제6호Some recurrence relations of multiple orthogonal polynomials이동원대한수학회 · 대한수학회지2005 · 제42권 제4호Finite orthogonal polynomials satisfying a second order differential equation유병훈, 이동원대한수학회 · 대한수학회논문집2005 · 제20권 제4호A difference equation for multiple Kravchuk polynomials이동원대한수학회 · 대한수학회지2007 · 제44권 제6호A differential equation for multiple Bessel polynomials with raising and lowering operators백진옥, 이동원대한수학회 · 대한수학회보2011 · 제48권 제3호Darboux transforms and orthogonal lynomials윤강준대한수학회 · 대한수학회보2002 · 제39권 제3호

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