Meixner polynomials
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11—20 of 25 matching pages
11: 15.9 Relations to Other Functions
12: Bibliography J
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Uniform asymptotic expansions for Meixner polynomials.
Constr. Approx. 14 (1), pp. 113–150.
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Asymptotic formulas for the zeros of the Meixner polynomials.
J. Approx. Theory 96 (2), pp. 281–300.
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13: Errata
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►We have significantly expanded the section on associated orthogonal polynomials, including expanded properties of associated Laguerre, Hermite, Meixner–Pollaczek, and corecursive orthogonal and numerator and denominator orthogonal polynomials.
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Equation (18.35.9)
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18.35.9
Previously we gave only the first identity .
14: Bibliography W
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Global asymptotics of the Meixner polynomials.
Asymptotic Analysis 75 (3-4), pp. 211–231.
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15: Bibliography K
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Uniform asymptotic approximations for the Meixner-Sobolev polynomials.
Anal. Appl. (Singap.) 10 (3), pp. 345–361.
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Meixner-Pollaczek polynomials and the Heisenberg algebra.
J. Math. Phys. 30 (4), pp. 767–769.
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16: Bibliography L
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On the asymptotics of the Meixner-Pollaczek polynomials and their zeros.
Constr. Approx. 17 (1), pp. 59–90.
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17: 18.2 General Orthogonal Polynomials
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►This happens, for example, with the continuous Hahn polynomials and Meixner–Pollaczek polynomials (§18.20(i)).
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►The generating functions (18.12.13), (18.12.15), (18.23.3), (18.23.4), (18.23.5) and (18.23.7) for Laguerre, Hermite, Krawtchouk, Meixner, Charlier and Meixner–Pollaczek polynomials, respectively, can be written in the form (18.2.45).
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18: Bibliography B
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Josef Meixner: his life and his orthogonal polynomials.
Indag. Math. (N.S.) 30 (1), pp. 250–264.
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19: Gerhard Wolf
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►Wolf has published papers on Mathieu functions, orthogonal polynomials, and Heun functions.
… Meixner and F.
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20: 28.34 Methods of Computation
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(e)
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(f)
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(d)
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Solution of the systems of linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4), with the conditions (28.4.9)–(28.4.12) and (28.14.5), by boundary-value methods (§3.6) to determine the Fourier coefficients. Subsequently, the Fourier series can be summed with the aid of Clenshaw’s algorithm (§3.11(ii)). See Meixner and Schäfke (1954, §2.87). This procedure can be combined with §28.34(ii)(d).