PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1998 | 78 | 1 | 57-91
Tytuł artykułu

On block recursions, Askey's sieved Jacobi polynomials and two related systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Two systems of sieved Jacobi polynomials introduced by R. Askey are considered. Their orthogonality measures are determined via the theory of blocks of recurrence relations, circumventing any resort to properties of the Askey-Wilson polynomials. The connection with polynomial mappings is examined. Some naturally related systems are also dealt with and a simple procedure to compute their orthogonality measures is devised which seems to be applicable in many other instances.
Rocznik
Tom
78
Numer
1
Strony
57-91
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-10-07
poprawiono
1998-01-22
Twórcy
  • Department of Mathematics and Statistics, National University of Colombia, Bogotá, Colombia
  • Department of Mathematics and Statistics, National University of Colombia, Bogotá, Colombia
  • School of Mathematics, City University of Bogotá, Francisco José de Caldas, Bogotá, Colombia
Bibliografia
  • [1] N. Al-Salam and M. E. H. Ismail, On sieved orthogonal polynomials VIII: Sieved associated Pollaczek polynomials, J. Approx. Theory 68 (1992), 306-321.
  • [2] W. Al-Salam, W. Allaway and R. Askey, Sieved ultraspherical polynomials, Trans. Amer. Math. Soc. 234 (1984), 39-55.
  • [3] G. Andrews, q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra, CBMS Regional Conf. Ser. in Math. 66, Amer. Math. Soc., Providence, R.I., 1986.
  • [4] R. Askey, Orthogonal polynomials old and new, and some combinatorial connections, in: Enumeration and Design, D. M. Jackson and S. A. Vanstone (eds.), Academic Press, Toronto, Ont., 1984, 67-84.
  • [5] R. Askey and M. E. H. Ismail, The Rogers q-ultraspherical polynomials, in: Approximation Theory III, E. W. Cheney (ed.), Academic Press, New York, N.Y., 1980, 175-182.
  • [6] R. Askey and M. E. H. Ismail, A generalization of the ultraspherical polynomials, in: Studies in Pure Mathematics, P. Erdős (ed.), Birkhäuser, Basel, 1983, 55-78.
  • [7] R. Askey and M. E. H. Ismail, Recurrence relations, continued fractions and orthogonal polynomials, Mem. Amer. Math. Soc. 300 (1984).
  • [8] R. Askey and J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 319 (1985).
  • [9] S. Belmehdi, On the left multiplication of a regular linear functional by a polynomial, in: Orthogonal Polynomials and Their Applications, IMACS Ann. Comput. Appl. Math. 9, Baltzer, Basel, 1991, 169-175.
  • [10] J. A. Charris and L. A. Gómez, On the orthogonality measure of the q-Pollaczek polynomials, Rev. Colombiana Mat. 21 (1987), 301-316.
  • [11] J. A. Charris and M. E. H. Ismail, On sieved orthogonal polynomials II: Random walk polynomials, Canad. J. Math. 38 (1986), 397-415.
  • [12] J. A. Charris and M. E. H. Ismail, On sieved orthogonal polynomials V: Sieved Pollaczek polynomials, SIAM J. Math. Anal. 18 (1987), 1177-1218.
  • [13] J. A. Charris and M. E. H. Ismail, Sieved orthogonal polynomials VII: Generalized polynomial mappings, Trans. Amer. Math. Soc. 340 (1993), 71-93.
  • [14] J. A. Charris, M. E. H. Ismail and S. Monsalve, Sieved orthogonal polynomials X: General blocks of recurrence relations, Pacific J. Math. 163 (1994), 1294-1308.
  • [15] J. A. Charris and Y. L. Prieto, On distributional representation of moment functionals: Sieved Pollaczek polynomials, Rev. Acad. Colombiana Cienc. 73 (1994), 305-315.
  • [16] J. A. Charris and F. Soriano, Complex and distributional weights for sieved ultraspherical polynomials, Internat. J. Math. Math. Sci. 19 (1996), 229-242.
  • [17] J. A. Charris and F. Soriano, On the distributional orthogonality of the general Pollaczek polynomials, ibid., 417-426.
  • [18] T. S. Chihara, On co-recursive orthogonal polynomials, Proc. Amer. Math. Soc. 8 (1957), 899-905.
  • [19] T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, N.Y., 1978.
  • [20] T. S. Chihara, On kernel polynomials and related systems, Boll. Un. Mat. Ital. (3) 19 (1964), 451-459
  • [21] J. Fields, A unified treatment of Darboux's method, Arch. Rational. Mech. Anal. 27 (1967/68), 289-305.
  • [22] G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia Math. Appl. 35, Cambridge Univ. Press, Cambridge, 1990.
  • [23] J. Geronimo and W. Van Assche, Orthogonal polynomials on several intervals via a polynomial mapping, Trans. Amer. Math. Soc. 308 (1988), 559-581.
  • [24] M. E. H. Ismail, Sieved orthogonal polynomials I: Symmetric Pollaczek analogues, SIAM J. Math. Anal. 16 (1985), 89-111.
  • [25] M. E. H. Ismail, Sieved orthogonal polynomials III: Orthogonality on several intervals, Trans. Amer. Math. Soc. 294 (1986), 89-111.
  • [26] M. E. H. Ismail and D. R. Masson, Two families of orthogonal polynomials related to the Jacobi polynomials, Rocky Mountain J. Math. 21 (1991), 359-375.
  • [27] M. E. H. Ismail, D. Masson and M. Rahman, Complex weight functions for classical orthogonal polynomials, Canad. J. Math. 43 (1991), 1294-1308.
  • [28] S. Lang, Real and Functional Analysis, 3rd ed., Springer, New York, N.Y., 1993.
  • [29] F. Marcellan, J. S. Dehesa and A. Ronveaux, On orthogonal polynomials with perturbed recurrence relations, J. Comput. Appl. Math. 30 (1990), 203-212.
  • [30] F. W. Olver, Asymptotics and Special Functions, Academic Press, New York, N.Y., 1974.
  • [31] E. D. Rainville, Special Functions, Macmillan, New York, N.Y., 1960.
  • [32] L. J. Rogers, On the expansion of some infinite products, Proc. London Math. Soc. 24 (1893), 337-352.
  • [33] L. J. Rogers, Second memoir on the expansion of some infinite products, ibid. 25 (1894), 318-342.
  • [34] L. J. Rogers, Third memoir on the expansion of some infinite products, ibid. 26 (1895), 15-32.
  • [35] L. J. Rogers, On two theorems of combinatory analysis and some allied identities, ibid. 16 (1917), 315-336.
  • [36] L. J. Rogers and S. Ramanujan, Proof of certain identities in combinatory analysis, Proc. Cambridge Philos. Soc. 19 (1919), 211-216.
  • [37] H. A. Slim, On co-recursive orthogonal polynomials and their application to potential scattering, J. Math. Anal. Appl. 136 (1988), 1-19.
  • [38] H. Stroud and D. Secrest, Gaussian Quadrature Formulas, Prentice Hall, Englewood Cliffs, N.J., 1966.
  • [39] G. Szegő, Ein Beitrag zur Theorie der Polynome von Laguerre und Jacobi, Math. Z. 1 (1918), 341-456.
  • [40] G. Szegő, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., 23, Amer. Math. Soc., Providence, R.I., 1975.
  • [41] H. S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, New York, N.Y., 1948.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv78z1p57bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.