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1996-1997 | 24 | 4 | 445-455
Tytuł artykułu

Linearization of the product of orthogonal polynomials of a discrete variable

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let {$P_k$} be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in $P_iP_j=\sum_kc(i,j,k)P_k$, in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by {$P_k$}.
Rocznik
Tom
24
Numer
4
Strony
445-455
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-11-07
Twórcy
  • UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq, France
  • Institute of Computer Science, University of Wrocław, 51-151 Wrocław, Poland
  • Laboratoire de Physique Mathématique Facultés Universitaires N.-D. de la Paix, B-5000 Namur, Belgium
Bibliografia
  • R. Askey, Orthogonal Polynomials and Special Functions, Regional Conf. Ser. Appl. Math. 21, SIAM, Philadelphia, 1975.
  • R. Askey and G. Gasper, Convolution structures for Laguerre polynomials, J. Anal. Math. 31 (1977), 48-68.
  • B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan and S. M. Watt, Maple V Language Reference Manual, Springer, New York, 1991.
  • T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
  • A. G. Garcia, F. Marcellán and L. Salto, A distributional study of discrete classical orthogonal polynomials, J. Comput. Appl. Math. 57 (1995), 147-162.
  • R. Koekoek and R. F. Swarttouw, The Askey scheme of hypergeometric orthogonal polynomials and its q-analogue, Fac. Techn. Math. Informatics, Delft Univ. of Technology, Rep. 94-05, Delft, 1994.
  • J. Letessier, A. Ronveaux and G. Valent, Fourth order difference equation for the associated Meixner and Charlier polynomials, J. Comput. Appl. Math. 71 (1996), 331-341.
  • S. Lewanowicz, Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable, ibid. 76 (1996), 213-229.
  • A. F. Nikiforov, S. K. Suslov and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991.
  • A. Ronveaux, S. Belmehdi, E. Godoy and A. Zarzo, Recurrence relations approach for connection coefficients-Applications to classical discrete orthogonal polynomials, in: Symmetries and Integrability of Difference Equations, D. Levi, L. Vinet and P. Winternitz (eds.), Centre de Recherches Mathématiques, CRM Proc. and Lecture Notes Ser. 9, Amer. Math. Soc., Providence, 1996, 321-337.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv24i4p445bwm
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