Charlier polynomials
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1—10 of 12 matching pages
1: 18.21 Hahn Class: Interrelations
2: 18.19 Hahn Class: Definitions
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Table 18.19.1: Orthogonality properties for Hahn, Krawtchouk, Meixner, and Charlier OP’s: discrete sets, weight functions, standardizations, and parameter constraints.
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Hahn, Krawtchouk, Meixner, and Charlier
►Tables 18.19.1 and 18.19.2 provide definitions via orthogonality and standardization (§§18.2(i), 18.2(iii)) for the Hahn polynomials , Krawtchouk polynomials , Meixner polynomials , and Charlier polynomials . ►… | ||||
Charlier | , |
3: 18.22 Hahn Class: Recurrence Relations and Differences
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Table 18.22.1: Recurrence relations (18.22.2) for Krawtchouk, Meixner, and Charlier polynomials.
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Table 18.22.2: Difference equations (18.22.12) for Krawtchouk, Meixner, and Charlier polynomials.
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18.22.25
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18.22.26
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4: 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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18.20.8
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5: 18.23 Hahn Class: Generating Functions
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18.23.5
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6: 18.24 Hahn Class: Asymptotic Approximations
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►Dunster (2001b) provides various asymptotic expansions for as , in terms of elementary functions or in terms of Bessel functions.
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7: 13.6 Relations to Other Functions
8: 18.1 Notation
9: Bibliography D
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Uniform asymptotic expansions for Charlier polynomials.
J. Approx. Theory 112 (1), pp. 93–133.
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10: Bibliography G
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Plancherel-Rotach asymptotics for the Charlier polynomials.
Constr. Approx. 14 (2), pp. 151–168.
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