disk polynomials
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1: 18.37 Classical OP’s in Two or More Variables
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§18.37(i) Disk Polynomials
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18.37.2
and/or .
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►The following three conditions, taken together, determine uniquely:
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18.37.3
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18.37.5
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2: 18.1 Notation
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Disk: .
3: Bibliography C
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Stability properties of disk polynomials.
Numer. Algorithms.
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4: 18.38 Mathematical Applications
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►also the case of (18.14.26), was used in de Branges’ proof of the long-standing Bieberbach conjecture concerning univalent functions on the unit disk in the complex plane.
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5: 16.2 Definition and Analytic Properties
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►Then the series (16.2.1) terminates and the generalized hypergeometric function is a polynomial in .
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►If none of the is a nonpositive integer, then the radius of convergence of the series (16.2.1) is , and outside the open disk
the generalized hypergeometric function is defined by analytic continuation with respect to .
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Polynomials
… ►However, when one or more of the top parameters is a nonpositive integer the series terminates and the generalized hypergeometric function is a polynomial in . … ►Non-Polynomials
…6: Bibliography B
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The generating function of Jacobi polynomials.
J. London Math. Soc. 13, pp. 8–12.
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The Calculation of Spherical Bessel Functions and Coulomb Functions.
In Computational Atomic Physics: Electron and Positron Collisions
with Atoms and Ions, K. Bartschat and J. Hinze (Eds.),
pp. 181–202.
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A generalisation of the Legendre polynomial.
Proc. London Math. Soc. (2) 3 (3), pp. 111–123.
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Polynomials defined by a difference system.
J. Math. Anal. Appl. 2 (2), pp. 223–263.
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Extrapolation Methods. Theory and Practice.
Studies in Computational Mathematics, Vol. 2, North-Holland Publishing Co., Amsterdam.
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7: Bibliography L
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A Numerical Library in C for Scientists and Engineers.
CRC Press, Boca Raton, FL.
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The real zeros of the Bernoulli polynomials.
J. Approx. Theory 58 (2), pp. 124–150.
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On the maxima and minima of Bernoulli polynomials.
Amer. Math. Monthly 47 (8), pp. 533–538.
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Approximation of orthogonal polynomials in terms of Hermite polynomials.
Methods Appl. Anal. 6 (2), pp. 131–146.
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Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials.
J. Math. Anal. Appl. 239 (2), pp. 457–477.
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8: Bibliography W
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Global asymptotics of the Meixner polynomials.
Asymptotic Analysis 75 (3-4), pp. 211–231.
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Asymptotics of orthogonal polynomials via recurrence relations.
Anal. Appl. (Singap.) 10 (2), pp. 215–235.
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Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach.
J. Math. Pures Appl. (9) 85 (5), pp. 698–718.
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Mathematical Software for the P.C. and Work Stations – A Collection of Fortran 77 Programs.
North-Holland Publishing Co., Amsterdam.
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Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials.
Ph.D. Thesis, University of Wisconsin, Madison, WI.
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9: 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 general mode theory for the elliptic disk microstrip antenna.
IEEE Trans. Antennas and Propagation 43 (6), pp. 560–568.
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A primer on Bernoulli numbers and polynomials.
Math. Mag. 81 (3), pp. 178–190.
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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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10: Bibliography P
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Zonal Polynomials of Order Through
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In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.),
Vol. 2, pp. 199–388.
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Orthogonal polynomials and some -beta integrals of Ramanujan.
J. Math. Anal. Appl. 112 (2), pp. 517–540.
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A new basis for the representation of the rotation group. Lamé and Heun polynomials.
J. Mathematical Phys. 14 (8), pp. 1130–1139.
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A K Peters Ltd., Wellesley, MA.
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Chebyshev polynomial expansions of the Riemann zeta function.
Math. Comp. 26 (120), pp. G1–G5.
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