Meixner polynomials
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21: 28.9 Zeros
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►For the zeros of and approach asymptotically the zeros of , and the zeros of and approach asymptotically the zeros of .
Here denotes the Hermite polynomial of degree (§18.3).
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►For further details see McLachlan (1947, pp. 234–239) and Meixner and Schäfke (1954, §§2.331, 2.8, 2.81, and 2.85).
22: Bibliography
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Some orthogonal -polynomials.
Math. Nachr. 30, pp. 47–61.
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Zeros of Stieltjes and Van Vleck polynomials.
Trans. Amer. Math. Soc. 252, pp. 197–204.
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A primer on Bernoulli numbers and polynomials.
Math. Mag. 81 (3), pp. 178–190.
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A new treatment of the ellipsoidal wave equation.
Proc. London Math. Soc. (3) 9, pp. 21–50.
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Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials.
Mem. Amer. Math. Soc. 54 (319), pp. iv+55.
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23: Bibliography S
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Über einige Integrale mit Produkten von Mathieu-Funktionen.
Arch. Math. (Basel) 41 (2), pp. 152–162.
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Uniform asymptotic expansions of modified Mathieu functions.
J. Reine Angew. Math. 247, pp. 1–17.
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Some properties of polynomial sets of type zero.
Duke Math. J. 5, pp. 590–622.
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Prolate spheroidal wave functions, Fourier analysis and uncertainity. IV. Extensions to many dimensions; generalized prolate spheroidal functions.
Bell System Tech. J. 43, pp. 3009–3057.
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Szegő polynomials from hypergeometric functions.
Proc. Amer. Math. Soc. 138 (12), pp. 4259–4270.
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24: Bibliography M
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Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion.
J. Lond. Math. Soc. 9, pp. 6–13 (German).
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Mathieu Functions and Spheroidal Functions and Their Mathematical Foundations: Further Studies.
Lecture Notes in Mathematics, Vol. 837, Springer-Verlag, Berlin-New York.
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Klassifikation, Bezeichnung und Eigenschaften der Sphäroidfunktionen.
Math. Nachr. 5, pp. 1–18 (German).
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Die Laméschen Wellenfunktionen des Drehellipsoids.
Forschungsbericht No. 1952
ZWB (German).
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Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers.
J. Reine Angew. Math. 211, pp. 33–47.
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