Pollaczek polynomials
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1: 18.35 Pollaczek Polynomials
2: 18.24 Hahn Class: Asymptotic Approximations
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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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3: 18.21 Hahn Class: Interrelations
4: 18.22 Hahn Class: Recurrence Relations and Differences
5: 18.19 Hahn Class: Definitions
6: 18.20 Hahn Class: Explicit Representations
7: 18.1 Notation
8: 18.23 Hahn Class: Generating Functions
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18.23.7
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9: 18.30 Associated OP’s
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►The type 3 Pollaczek polynomials are the associated type 2 Pollaczek polynomials, see §18.35.
The relationship (18.35.8) implies the definition for the associated ultraspherical polynomials
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§18.30(v) Associated Meixner–Pollaczek Polynomials
►In view of (18.22.8) the associated Meixner–Pollaczek polynomials are defined by the recurrence relation ►10: 18.39 Applications in the Physical Sciences
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►Thus the and the eigenvalues
…are determined by the zeros, of the Pollaczek polynomial
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The Coulomb–Pollaczek Polynomials
►The polynomials , for both positive and negative , define the Coulomb–Pollaczek polynomials (CP OP’s in what follows), see Yamani and Reinhardt (1975, Appendix B, and §IV). … ►
18.39.54
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