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SOME RECURRENCE RELATIONS OF MULTIPLE ORTHOGONAL POLYNOMIALS
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 Title & Authors
SOME RECURRENCE RELATIONS OF MULTIPLE ORTHOGONAL POLYNOMIALS
Lee, Dong-Won;
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 Abstract
In this paper, we first find a necessary and sufficient condition for the existence of multiple orthogonal polynomials by the moments of a pair of measures and then give representations for multiple orthogonal polynomials. We also prove four term recurrence relations for multiple orthogonal polynomials of type II and several interesting relations for multiple orthogonal polynomials are given. A generalized recurrence relation for multiple orthogonal polynomials of type I is found and then four term recurrence relations are obtained as a special case.
 Keywords
orthogonal polynomials;multiple orthogonal polynomials;recurrence relation;
 Language
English
 Cited by
1.
A DIFFERENCE EQUATION FOR MULTIPLE KRAVCHUK POLYNOMIALS,;

대한수학회지, 2007. vol.44. 6, pp.1429-1440 crossref(new window)
 References
1.
A. Angelesco, Sur l'approximation simultanee de plusieurs integrales definies, C. R. Math. Acad. Sci. Paris 167 (1918), 629-631

2.
A. I. Aptekarev, Multiple orthogonal polynomials, J. Comput. Appl. Math. 99 (1998), 423-447 crossref(new window)

3.
A. I. Aptekarev, A. Branquinho, and W. Van Assche, Multiple orthogonal polynomials for classical weights, Trans. Amer. Math. Soc. 355 (2003), 3887-3914 crossref(new window)

4.
A. I. Aptekarev and H. Stahl, Asymptotics of Hermite-Pade polynomials, Progress in Approximation Theory, in A. Gonchar and E.B. Saff (Eds.) Springer Ser. Comput. Math. 19 (1992), 127-167 crossref(new window)

5.
J. Arvesu, J. Coussement, and W. Van Assche, Some discrete multiple orthogonal polynomials, J. Comput. Appl. Math. 153 (2003), 19-45 crossref(new window)

6.
B. Beckermann, J. Coussement, and W. Van Assche, Multiple Wilson and Jacobi-Pineiro polynomials, J. Approx. Theory 132 (2005), 155-181 crossref(new window)

7.
C. Brezinski and J. Van Iseghem, Vector orthogonal polynomials of dimension -d, Approximation and computation (West Lafayette, IN, 1993), Internat. Ser. Numer. Math. 119 (1994), 29-39

8.
M. G. de Bruin, Simultaneous Pade approximants and orthogonality, Lecture Notes in Math. 1171 (1985), 74-83 crossref(new window)

9.
J. Coussement and W. Van Assche, Gauss quadrature for multiple orthogonal polynomials, J. Comput. Appl. Math. 178 (2005), 131-145 crossref(new window)

10.
V. A. Kalyagin, Hermite-Pade approximants and spectral analysis of nonsymmetric operators, Mat. Sb. 185 (1994), 79-100

11.
V. A. Kalyagin, Hermite-Pade approximants and spectral analysis of nonsymmetric operators, Sb. Mat. 82 (1995), 199-1216 crossref(new window)

12.
K. Mahler, Perfect systems, Compositio Math. 19 (1968), 95-166

13.
E. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality, Trans. Amer. Math. Soc. 92 (1991)

14.
V. N. Sorokin and J. Van Iseghem, Algebraic aspects of matrix orthogonality for vector polynomials, J. Approx. Theory 90 (1997), 97-116 crossref(new window)

15.
W. Van Assche and E. Coussement, Some classical multiple orthogonal polyno-mials, J. Comput. Appl. Math. 127 (2001), 317-347 crossref(new window)

16.
J. Van Iseghem, Recurrence relations in the table of vector orthogonal polynomi- als, Nonlinear Numerical Methods and Rational Approximation II, Math. Appl. 296 (1994), 61-69