as associated type 2 Pollaczek polynomials
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6 matching pages
1: 18.30 Associated OP’s
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►They can be expressed in terms of type 3 Pollaczek polynomials (which are also associated type 2 Pollaczek polynomials) by (18.35.10).
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►The type 3 Pollaczek polynomials are the associated type 2 Pollaczek polynomials, see §18.35.
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2: 18.35 Pollaczek Polynomials
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►As in the coefficients of the above recurrence relations and only occur in the form , the type 3 Pollaczek polynomials may also be called the associated type 2 Pollaczek polynomials by using the terminology of §18.30.
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3: Bibliography B
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On the Associated Legendre Polynomials.
In Orthogonal Expansions and their Continuous Analogues (Proc.
Conf., Edwardsville, Ill., 1967),
pp. 43–50.
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Tables of Normalized Associated Legendre Polynomials.
Pergamon Press, The Macmillan Co., Oxford-New York.
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Asymptotic behavior of the Pollaczek polynomials and their zeros.
Stud. Appl. Math. 96, pp. 307–338.
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A uniform asymptotic formula for orthogonal polynomials associated with
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J. Approx. Theory 98, pp. 146–166.
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Padé-type Approximation and General Orthogonal Polynomials.
International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
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4: 18.39 Applications in the Physical Sciences
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§18.39(iv) Coulomb–Pollaczek Polynomials and J-Matrix Methods
… ►The recursion of (18.39.46) is that for the type 2 Pollaczek polynomials of (18.35.2), with , , and , and terminates for being a zero of the polynomial of order . …are determined by the zeros, of the Pollaczek polynomial . ►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). …5: Bibliography P
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A Kummer-type transformation for a hypergeometric function.
J. Comput. Appl. Math. 173 (2), pp. 379–382.
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Sur une généralisation des polynomes de Legendre.
C. R. Acad. Sci. Paris 228, pp. 1363–1365.
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Systèmes de polynomes biorthogonaux qui généralisent les polynomes ultrasphériques.
C. R. Acad. Sci. Paris 228, pp. 1998–2000.
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Sur une famille de polynômes orthogonaux à quatre paramètres.
C. R. Acad. Sci. Paris 230, pp. 2254–2256.
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Voronoi type congruences for Bernoulli numbers.
In Voronoi’s Impact on Modern Science. Book I, P. Engel and H. Syta (Eds.),
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6: 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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