Gegenbauer%20polynomials
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1: 18.5 Explicit Representations
§18.5 Explicit Representations
… ►Laguerre
… ►Similarly in the cases of the ultraspherical polynomials and the Laguerre polynomials we assume that , and , unless stated otherwise. … ►2: Bibliography C
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New proof of the addition theorem for Gegenbauer polynomials.
SIAM J. Math. Anal. 2, pp. 347–351.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems.
SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 042, 26.
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On a generalization of the generating function for Gegenbauer polynomials.
Integral Transforms Spec. Funct. 24 (10), pp. 807–816.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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3: 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.
4: Bibliography K
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Orthogonal Polynomials on -spheres: Gegenbauer, Jacobi and Heun.
In Topics in Polynomials of One and Several Variables and their
Applications,
pp. 299–322.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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5: 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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Nicholson-type Integrals for Products of Gegenbauer Functions and Related Topics.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975), R. A. Askey (Ed.),
pp. 353–374. Math. Res. Center, Univ. Wisconsin, Publ. No. 35.
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