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Darboux transforms and orthogonal lynomials
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Abstract
We give a new interpretation of Darboux transforms in the contextof orthogonal polynomials and find conditions in order for anyDarboux transform to yield a new set of orthogonal polynomials.We also discuss connections between Darboux transforms andfactorization of linear differential operators which haveorthogonal polynomial eigenfunctions.
관련 논문AI추천
Some recurrence relations of multiple orthogonal polynomials이동원대한수학회 · 대한수학회지2005 · 제42권 제4호Partial differential equations for products of two classical orthogonal polynomials이동원대한수학회 · 대한수학회보2005 · 제42권 제1호Finite orthogonal polynomials satisfying a second order differential equation유병훈, 이동원대한수학회 · 대한수학회논문집2005 · 제20권 제4호A difference equation for multiple Kravchuk polynomials이동원대한수학회 · 대한수학회지2007 · 제44권 제6호Orthogonal polynomials satisfying partial differential equations belonging to the basic class유병훈, J. K. Lee, L. L. Littlejohn대한수학회 · 대한수학회지2004 · 제41권 제6호The recurrence coefficients of the orthogonal polynomials with the weights $w_\alpha(x)= x^\alpha \exp(-x^3+tx)$ and $W_\alpha(x)=|x|^{2\alpha+1} \exp(-x^6+tx^2)$정해원강원경기수학회 · 한국수학논문집2017 · 제25권 제2호
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