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A DIFFERENCE EQUATION FOR MULTIPLE KRAVCHUK POLYNOMIALS
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 Title & Authors
A DIFFERENCE EQUATION FOR MULTIPLE KRAVCHUK POLYNOMIALS
Lee, Dong-Won;
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 Abstract
Let be a multiple Kravchuk polynomial with respect to r discrete Kravchuk weights. We first find a lowering operator for multiple Kravchuk polynomials in which the orthogonalizing weights are not involved. Combining the lowering operator and the raising operator by Rodrigues# formula, we find a (r+1)-th order difference equation which has the multiple Kravchuk polynomials as solutions. Lastly we give an explicit difference equation for for the case of r=2.
 Keywords
multiple orthogonal polynomials;Kravchuk polynomials;difference equation;rodrigues' formula;
 Language
English
 Cited by
1.
Difference equations for discrete classical multiple orthogonal polynomials, Journal of Approximation Theory, 2008, 150, 2, 132  crossref(new windwow)
 References
1.
A. Angelesco, Sur l'approximation simultanee de plusieurs integrales definies, C. R. Paris, 167 (1918), 629-631

2.
A. I. Aptekarev, Multiple orthogonal polynomials, J. Comp. Appl. Math. 99 (1998), no. 1-2, 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), no. 10, 3887-3914 crossref(new window)

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

5.
J. Arvesu, J. Coussement, and W. Van Assche, Some discrete multiple orthogonal poly- nomials, J. Comp. Appl. Math. 153 (2003), no. 1-2, 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), no. 2, 155-181 crossref(new window)

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

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

9.
J. Coussement and W. Van Assche, Gaussian quadrature for multiple orthogonal poly- nomials, J. Comp. Appl. Math. 178 (2005), no. 1-2, 131-145 crossref(new window)

10.
V. A. Kalyagin, Hermite-Pade approximants and spectral analysis of nonsymmetric operators, Math. Sb. 185 (1994), no. 6, 79-100

11.
V. A. Kalyagin, Hermite-Pade approximants and spectral analysis of nonsymmetric operators, English transl. in. Russian Acad. Sci. Sb. Math. 82 (1995), no. 1, 199-216 crossref(new window)

12.
M. Krawtchouk, Sur Une Generalisation des Polynomes d'Hermite, C. R. Acad. Sci. 189 (1929), 620-622

13.
D. W. Lee, Some recurrence relations of multiple orthogonal polynomials, J. Korean Math. Soc. 42 (2005), no. 4, 673-693 crossref(new window)

14.
A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer-Verlag, Berlin, 1991

15.
E. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality, Trans- lations of Mathematical Monographs 92, Amer. Math. Soc., 1991

16.
K. Postelmans and W. Van Assche, Multiple little q-Jacobi polynomials, J. Comput. Appl. Math. 178 (2005), no. 1-2, 361-375 crossref(new window)

17.
G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Soc., Colloq. Publ. 23, Providence, RI, 1975

18.
W. Van Assche and E. Coussement, Some classical multiple orthogonal polynomials, J. Comp. Appl. Math. 127 (2001), no. 1-2, 317-347 crossref(new window)

19.
W. Van Assche, Difference equations for multiple Charlier and Meixner polynomials, in New Progress in Difference Equations (S. Elaydi et al. eds.), Taylor and Francis, London, (2004), 547-557

20.
J. Van Iseghem, Recurrence relations in the table of vector orthogonal polynomials, Nonlinear Numerical Methods and Rational Approximation II, Math. Appl., Kluwer Academic Publishers, Dordrecht, 296 (1994), 61-69