Orthogonal polynomial eigenfunctions of second-order partial differerential equations

Transactions of the American Mathematical Society

Volumn 353, Issue 9, 2001, Pages 3629-3647

  Kwon, K H ^a,c   Lee, J K ^b   Littlejohn, L L ^c  

^a Department of Mathematics ^*  (South Korea)

^b SunMoon University   (South Korea)

^c UTAH STATE UNIVERSITY   (United States)

Author keywords

Orthogonal polynomials in two variables; Second order partial differential equations

Indexed keywords

EID: 23044527799     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-01-02784-2     Document Type: Article

References (15)

1. P. Appell and J. K. de Fériet, Fonctions Hypergéometriques et Hypersphériques; Polynomes d'Hermite, Paris, Gauthier-Villars et Cie (1926).
2. V. K. Jain, On the orthogonal polynomials of two variables, Indian J. Pure Appl. Math. 11(4) (1980), 492-501. MR 81c:42030
3. Y. J. Kim, K. H. Kwon, and J. K. Lee, Orthogonal polynomials in two variables and second order partial differential equations, J. Comp. Appl. Math. 82 (1997), 239-260. MR 98m:33031
4. Y. J. Kim, K. H. Kwon, and J. K. Lee, Partial differential equations having orthogonal polynomial solutions, J. Comp. Appl. Math. 99 (1998) no. 1-2, 239-253. MR 99j:35007
5. T. H. Koornwinder, Two-variable analogues of the classical orthogonal polynomiah, Theory and Applications of Special Functions, R. Askey Ed., Academic Press (1975), 435-495. MR 53:5967
6. H. L. Krall and O. Frink; A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100-115. MR 10:453a
7. H. L. Krall and I. M. Sheffer, Orthogonal polynomials in two variables, Ann. Mat. Pura Appl. (4) 76 (1967), 325- 376. MR 37:4499
8. K. H. Kwon, S. S. Kim, and S. S. Han, Orthogonality of Tchebychev sets of polynomials, Bull. London Math. Soc. 24 (1992), 361-367. MR 93g:33007
9. K. H. Kwon, J. K. Lee, and B. H. Yoo, Characterizations of classical orthogonal polynomials, Results in Math. 24 (1993), 119-128. MR 981:33010
10. K. H. Kwon and L. L. Littlejohn, Classification of classical orthogonal polynomials, J. Korean Math. Soc., 34 (1997), 973-1008. MR 99k:35007
11. L. L. Littlejohn, Orthogonal polynomial solutions to ordinary and partial differential equations, Proc. 2nd Intern. Symp. Orthogonal Polynomial and their Applications, M. Alfaro et al. Eds, Segovia (Spain), 1986, Lect. Notes Math. Vol. 1329, Springer-Verlag, Berlin, 1988, 98-124. MR 89j:33013
12. F. Marcellán, A. Branquinho, and J. Petronilho, Classical orthogonal polynomials: A functional approach, Acta Appl. Math. 34 (1994), 283-303. MR 95b:33024
13. P. Maroni, An integral representation for the Bessel form, J. Comp. Appl. Math. 57 (1995), 251-260. MR 96a:42038
14. P. K. Suetin, Orthogonal polynomials in two variables, Nauka, Moscow, 1988 (in Russian). MR 90g:42055
15. Y. Xu, A class of bivariate orthogonal polynomials and cubature formula, Numer. Math. 69 (1994), 233-241. MR 96b:65027