ultraspherical%20polynomials
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1: 18.5 Explicit Representations
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►See (Erdélyi et al., 1953b, §10.9(37)) for a related formula for ultraspherical polynomials.
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§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
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… ►For corresponding formulas for Chebyshev, Legendre, and the Hermite polynomials apply (18.7.3)–(18.7.6), (18.7.9), and (18.7.11). … ►Similarly in the cases of the ultraspherical polynomials and the Laguerre polynomials we assume that , and , unless stated otherwise. …2: Errata
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Equation (18.7.25)
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Chapters 14 Legendre and Related Functions, 15 Hypergeometric Function
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Chapters 8, 20, 36
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Table 18.9.1
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References
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18.7.25
We included the case .
The coefficient for in the first row of this table originally omitted the parentheses and was given as , instead of .
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Reported 2010-09-16 by Kendall Atkinson.
3: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets.
SIAM J. Math. Anal. 30 (5), pp. 1029–1056.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3), pp. 21–56.
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4: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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On the relative extrema of ultraspherical polynomials.
Boll. Un. Mat. Ital. (3) 5, pp. 125–127.
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