Geodesic
Nonclassical Orthogonal Polynomials as Solutions to Second Order Differential Equations
Canadian mathematical bulletin, Tome 25 (1982) no. 3, pp. 291-295

Voir la notice de l'article provenant de la source Cambridge University Press

One of the more popular problems today in the area of orthogonal polynomials is the classification of all orthogonal polynomial solutions to the second order differential equation: In this paper, we show that the Laguerre type and Jacobi type polynomials satisfy such a second order equation.
DOI : 10.4153/CMB-1982-040-2
Mots-clés : 33A65 
Littlejohn, Lance L.; Shore, Samuel D. Nonclassical Orthogonal Polynomials as Solutions to Second Order Differential Equations. Canadian mathematical bulletin, Tome 25 (1982) no. 3, pp. 291-295. doi: 10.4153/CMB-1982-040-2
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[1] 1. Cole, R. H., Theory of Ordinary Differential Equations, Appleton-Century-Crofts, New York, 1968. Google Scholar

[2] 2. Hahn, W., On Differential Equations for Orthogonal Polynomials, Funkcialaj Ekvacioj, Vol. 21 (1978), 1-9. Google Scholar

[3] 3. Krall, A. M., Orthogonal Polynomials Satisfying Fourth Order Differential Equations, Proc. Royal Soc. Edin. (to appear). Google Scholar

[4] 4. Krall, A. M. and Morton, R. D., Distributional Weight Functions for Orthogonal Polyonmials, S.I.A.M. J. Math. Anal., 4 (1978), 604-626: Google Scholar

[5] 5. Krall, H. L., On Orthogonal Polynomials satisfying a certain Fourth Order Differential Equation, The Pennsylvania State College Studies, No. 6, The Pennsylvania State College, State College, PA, 1940. Google Scholar

[6] 6. Shore, S. D., On the Sets of Orthogonal Polynomials which satisfy a Second Order Differential Equation, The Pennsylvania State University, Master's Thesis, 1961. Google Scholar

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