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quotient-difference scheme

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1: 3.10 Continued Fractions
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Quotient-Difference Algorithm
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Table 3.10.1: Quotient-difference scheme.
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… ►We continue by means of the rhombus rule … ► …
2: Bibliography S
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  • A. N. Stokes (1980) A stable quotient-difference algorithm. Math. Comp. 34 (150), pp. 515–519.
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    External Links:
    ISSN 0025-5718, FullText, MathReview, ZentralBlatt
    Referenced by:
    §3.10(ii).
    Encodings:
    BibTeX
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  • R. F. Swarttouw (1997) A computer implementation of the Askey-Wilson scheme. Technical Report 13 Vrije Universteit Amsterdam.
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    External Links:
    FullText
    Referenced by:
    CAOP (website).
    Encodings:
    BibTeX
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    3: 1.11 Zeros of Polynomials
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    Horner’s Scheme
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    Extended Horner Scheme
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    4: 7.22 Methods of Computation
    … ►The recursion scheme given by (7.18.1) and (7.18.7) can be used for computing i n ⁢ erfc ⁡ ( x ) . …
    5: 8.25 Methods of Computation
    … ►Stable recursive schemes for the computation of E p ⁡ ( x ) are described in Miller (1960) for x > 0 and integer p . …
    6: 16.24 Physical Applications
    … ►The coefficients of transformations between different coupling schemes of three angular momenta are related to the Wigner 6 ⁢ j symbols. …
    7: 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. …
    8: 6.20 Approximations
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    Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric U -function (§13.2(i)) from which Chebyshev expansions near infinity for E 1 ⁡ ( z ) , f ⁡ ( z ) , and g ⁡ ( z ) 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 U functions. If | ph ⁡ z | < π the scheme can be used in backward direction.

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    9: 18.21 Hahn Class: Interrelations
    … ►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. ►
    ►See accompanying text►
    Figure 18.21.1: Askey scheme. …It increases by one for each row ascended in the scheme, culminating with four free real parameters for the Wilson and Racah polynomials. … Magnify
    10: About Color Map
    … ►The four color scheme quickly indicates in which quadrant z lies: the colors blue, green, red and yellow are used to indicate the first, second, third and fourth quadrants, respectively. …
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