Al-Salam%E2%80%93Chihara%20polynomials
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21: 8.23 Statistical Applications
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►In queueing theory the Erlang loss function is used, which can be expressed in terms of the reciprocal of ; see Jagerman (1974) and Cooper (1981, pp. 80, 316–319).
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22: 26.13 Permutations: Cycle Notation
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23: 26.6 Other Lattice Path Numbers
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Table 26.6.1: Delannoy numbers .
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10 | 1 | 21 | 221 | 1561 | 8361 | 36365 | 1 34245 | 4 33905 | 12 56465 | 33 17445 | 80 97453 |
24: Bibliography J
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Fonctions de Mathieu et polynômes de Klein-Gordon.
C. R. Acad. Sci. Paris Sér. I Math. 325 (7), pp. 713–716 (French).
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Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent.
Phys. D 1 (1), pp. 80–158.
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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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Modifications of Coulombic interactions by polarizable atoms.
Math. Proc. Cambridge Philos. Soc. 80 (3), pp. 535–539.
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25: 1.11 Zeros of Polynomials
§1.11 Zeros of Polynomials
… ►Horner’s Scheme
… ►§1.11(ii) Elementary Properties
… ►The discriminant of is defined by … ►§1.11(v) Stable Polynomials
…26: 18.5 Explicit Representations
27: 18 Orthogonal Polynomials
Chapter 18 Orthogonal Polynomials
…28: 36.5 Stokes Sets
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36.5.4
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36.5.7
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►For the second sheet is generated by a second solution of (36.5.6)–(36.5.9), and for it is generated by the roots of the polynomial equation
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29: 22.7 Landen Transformations
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30: 9.18 Tables
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Miller (1946) tabulates , for , for ; , for ; , for ; , , , (respectively , , , ) for . Precision is generally 8D; slightly less for some of the auxiliary functions. Extracts from these tables are included in Abramowitz and Stegun (1964, Chapter 10), together with some auxiliary functions for large arguments.
Zhang and Jin (1996, p. 337) tabulates , , , for to 8S and for to 9D.
Sherry (1959) tabulates , , , , ; 20S.
Zhang and Jin (1996, p. 339) tabulates , , , , , , , , ; 8D.