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Askey scheme for orthogonal polynomials

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1: 18.21 Hahn Class: Interrelations
See accompanying text
Figure 18.21.1: Askey scheme. … Magnify
2: Richard A. Askey
Published in 1985 in the Memoirs of the American Mathematical Society, it also introduced the directed graph of hypergeometric orthogonal polynomials commonly known as the Askey scheme. …
3: Bibliography T
  • N. M. Temme and J. L. López (2001) The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis. J. Comput. Appl. Math. 133 (1-2), pp. 623–633.
  • 4: Bibliography K
  • R. Koekoek and R. F. Swarttouw (1998) The Askey-scheme of hypergeometric orthogonal polynomials and its q -analogue. Technical report Technical Report 98-17, Delft University of Technology, Faculty of Information Technology and Systems, Department of Technical Mathematics and Informatics.
  • 5: 18.26 Wilson Class: Continued
    Moreover, if one or more of the new parameters becomes zero, then the polynomial descends to a lower family in the Askey scheme.
    6: Bibliography C
  • CAOP (website) Work Group of Computational Mathematics, University of Kassel, Germany.
  • 7: Bibliography S
  • H. E. Salzer (1955) Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms. Math. Tables Aids Comput. 9 (52), pp. 164–177.
  • B. Simon (2005a) Orthogonal Polynomials on the Unit Circle. Part 1: Classical Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.
  • B. Simon (2005b) Orthogonal Polynomials on the Unit Circle. Part 2: Spectral Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.
  • R. F. Swarttouw (1997) A computer implementation of the Askey-Wilson scheme. Technical Report 13 Vrije Universteit Amsterdam.
  • G. Szegő (1967) Orthogonal Polynomials. 3rd edition, American Mathematical Society, New York.