Meixner polynomials
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1: 18.24 Hahn Class: Asymptotic Approximations
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►For two asymptotic expansions of as , with and fixed, see Jin and Wong (1998) and Wang and Wong (2011).
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►For asymptotic approximations for the zeros of in terms of zeros of (§9.9(i)), see Jin and Wong (1999) and Khwaja and Olde Daalhuis (2012).
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►For an asymptotic expansion of as , with fixed, see Li and Wong (2001).
…Corresponding approximations are included for the zeros of .
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►For asymptotic approximations to as , with fixed, see Temme and López (2001).
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2: 18.21 Hahn Class: Interrelations
3: 18.22 Hahn Class: Recurrence Relations and Differences
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Table 18.22.2: Difference equations (18.22.12) for Krawtchouk, Meixner, and Charlier polynomials.
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18.22.7
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18.22.16
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18.22.29
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18.22.30
4: 18.19 Hahn Class: Definitions
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►Tables 18.19.1 and 18.19.2 provide definitions via orthogonality and normalization (§§18.2(i), 18.2(iii)) for the Hahn polynomials
, Krawtchouk polynomials
, Meixner polynomials
, and Charlier polynomials
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Table 18.19.1: Orthogonality properties for Hahn, Krawtchouk, Meixner, and Charlier OP’s: discrete sets, weight functions, normalizations, and parameter constraints.
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18.19.6
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5: 18.20 Hahn Class: Explicit Representations
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►For the Krawtchouk, Meixner, and Charlier polynomials, and are as in Table 18.20.1.
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18.20.4
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18.20.7
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18.20.10