Upward extension of the Jacobi matrix for orthogonal polynomials

Journal of Approximation Theory

Volumn 86, Issue 3, 1996, Pages 335-357

  Ronveaux, André ^a   Van Assche, Walter ^b  

^a UNIVERSITY OF NAMUR   (Belgium)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030243463     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1996.0074     Document Type: Article

References (26)

1. 1. S. Belmehdi, On the associated orthogonal polynomials, J. Comput. Appl. Math. 32 (1990), 311-319.
2. 2. T. S. Chihara, "An Introduction to Orthogonal Polynomials," Gordon and Breach, New York, 1978.
3. 3. J. Dombrowski and P. Nevai, Orthogonal polynomials, measures and recurrence relations, SIAM J. Math. Anal. 17 (1986), 752-759.
4. 4. J. S. Geronimo and K. M. Case, Scattering theory and polynomials orthogonal on the real line, Trans. Amer. Math. Soc. 258 (1980), 467-494.
5. 5. J. S. Geronimo and W. Van Assche, Orthogonal polynomials with asymptotically periodic recurrence coefficients, J. Approx. Theory 46 (1986), 251-283.
6. 6. Ya. L. Geronimus, On some finite difference equations and corresponding systems of orthogonal polynomials, Zap. Mat. Otd. Fiz.-Mat. Fak. i Kharkov Mat. Obsc. 25, No. 4 (1957), 87-100 [in Russian].
7. 7. C. C. Grosjean, The measure induced by orthogonal polynomials satisfying a recursion formula with either constant or periodic coefficients. I. Constant coefficients, Acad. Analecta, Koninkl. Acad. Wetensch. Lett. Sch. Kunsten België 48, No. 3, (1986), 39-60.
8. 8. C. C. Grosjean, The measure induced by orthogonal polynomials satisfying a recursion formula with either constant or periodic coefficients. II. Pure or mixed periodic coefficients, Acad. Analecta, Koninkl. Acad. Wetensch. Lett. Sch. Kunsten België 48, No. 5 (1986), 57-94.
9. 9. C. C. Grosjean, The weight functions, generating functions and miscellaneous properties of the sequences of orthogonal polynomials of the second kind associated with the Jacobi and Gegenbauer polynomials, J. Comput. Appl. Math. 16 (1986), 259-307.
10. 10. S. Lewanowicz, Properties of the polynomials associated with the Jacobi polynomials, Math. Comp. 47 (1986), 669-682.
11. 11. F. Marcellán, J. S. Dehesa, and A. Ronveaux, On orthogonal polynomials with perturbed recurrence relations, J. Comput Appl. Math. 30 (1990), 203-212.
12. 12. A. Máté, P. Nevai and V. Totik, Szego's extremum problem on the unit circle, Ann. of Math. 134 (1991), 433-453.
13. 13. P. G. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc. 213, (1979).
14. 14. P. Nevai, A new class of orthogonal polynomials, Proc. Amer. Math. Soc. 91 (1984), 409-415.
15. 15. P. Nevai and W. Van Assche, Compact perturbations of orthogonal polynomials, Pacific J. Math. 153 (1992), 163-184.
16. 16. F. Peherstorfer, Finite perturbations of orthogonal polynomials, J. Comput. Appl. Math. 44 (1992), 275-302.
17. 17. A. Ronveaux, Fourth order differential equations for numerator polynomials, J. Phys. A 21 (1988), 749-753.
18. 18. A. Ronveaux, 4th order differential equations and orthogonal polynomials of the Laguerre-Hahn class, in "Orthogonal Polynomials and their Applications" (C. Brezinski et al., Eds.), IMACS Annals of Computing and Applied Mathematics, Vol. 9, pp. 379-385, Baltzer AG, Basel, 1991.
19. 19. A. Ronveaux, On a "first integral" relating classical orthogonal polynomials and their numerator polynomials, Simon Stevin 66 (1992), 159-171.
20. 20. A. Ronveaux, A. Zarzo, and E. Godoy, Fourth order differential equations satisfied by the generalized co-recursive of all classical orthogonal polynomials. A study of their distribution of zeros, J. Comput. Appl. Math. 59 (1995), 295-328.
21. 21. G. Sansigre and G. Valent, A large family of semi-classical polynomials: the perturbed Tchebichev, J. Comput. Appl. Math. 57 (1995), 271-281.
22. 22. G. Szego, "Orthogonal Polynomials," 4th edition, Amer. Math. Soc. Colloq. Publ., Vol. 23, Providence, RI, 1975.
23. 23. W. Van Assche, Orthogonal polynomials, associated polynomials and functions of the second kind, J. Comput. Appl. Math. 37 (1991), 237-249.
24. 24. W. Van Assche, Asymptotics for orthogonal polynomials and three-term recurrence, in "Orthogonal Polynomials: Theory and Practice" (P. Nevai, Ed.), NATO ASI Series C, Vol. 294, pp. 435-462, Kluwer, Dordrecht, 1990.
25. 25. V. V. Zabelin, Polynomial properties, Vestnik Moskov. Univ. Ser. 1, Mat. Mekh. 1 (1989), 98-100 [in Russian]; Mosc. Univ. Math. Bull. 44 (1989), 88-91.
26. 25. V. V. Zabelin, Polynomial properties, Vestnik Moskov. Univ. Ser. 1, Mat. Mekh. 1 (1989), 98-100 [in Russian]; Mosc. Univ. Math. Bull. 44 (1989), 88-91.