q-Askey scheme
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1—10 of 29 matching pages
1: 1.11 Zeros of Polynomials
2: 7.22 Methods of Computation
3: 8.25 Methods of Computation
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►Stable recursive schemes for the computation of are described in Miller (1960) for and integer .
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4: 16.24 Physical Applications
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►The coefficients of transformations between different coupling schemes of three angular momenta are related to the Wigner symbols.
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5: Richard A. Askey
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►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.
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6: 6.20 Approximations
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Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric -function (§13.2(i)) from which Chebyshev expansions near infinity for , , and follow by using (6.11.2) and (6.11.3). Luke also includes a recursion scheme for computing the coefficients in the expansions of the functions. If the scheme can be used in backward direction.
7: 18.21 Hahn Class: Interrelations
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►A graphical representation of limits in §§18.7(iii), 18.21(ii), and 18.26(ii) is provided by the Askey
scheme depicted in Figure 18.21.1.
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8: About Color Map
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►The four color scheme quickly indicates in which quadrant lies: the colors blue, green, red and yellow are used to indicate the first, second, third and fourth quadrants, respectively.
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9: 3.10 Continued Fractions
10: 18.38 Mathematical Applications
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►Similar algebras can be associated with all families of OP’s in the -Askey scheme and the Askey scheme.
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►Dunkl type operators and nonsymmetric polynomials have been associated with various other families in the Askey scheme and -Askey scheme, in particular with Wilson polynomials, see Groenevelt (2007), and with Jacobi polynomials, see Koornwinder and Bouzeffour (2011, §7).
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