continuous%20Hahn%20polynomials
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11: 18.20 Hahn Class: Explicit Representations
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§18.20(i) Rodrigues Formulas
… โบFor the Hahn polynomials and … โบContinuous Hahn
… โบ§18.20(ii) Hypergeometric Function and Generalized Hypergeometric Functions
… โบ(For symmetry properties of with respect to , , , see Andrews et al. (1999, Corollary 3.3.4).) …12: 18.22 Hahn Class: Recurrence Relations and Differences
13: 18.23 Hahn Class: Generating Functions
§18.23 Hahn Class: Generating Functions
… โบHahn
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18.23.1
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Continuous Hahn
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18.23.6
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14: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Continuous Hahn polynomials.
J. Phys. A 18 (16), pp. L1017–L1019.
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Continuous
-Hermite Polynomials when
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In
-series and Partitions (Minneapolis, MN, 1988),
IMA Vol. Math. Appl., Vol. 18, pp. 151–158.
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15: 20 Theta Functions
Chapter 20 Theta Functions
…16: 6.16 Mathematical Applications
17: Bibliography F
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Multivariate Calculation. Use of the Continuous Groups.
Springer Series in Statistics, Springer-Verlag, New York.
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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From continuous to discrete Painlevé equations.
J. Math. Anal. Appl. 180 (2), pp. 342–360.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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18: 18.28 Askey–Wilson Class
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§18.28(v) Continuous -Ultraspherical Polynomials
… โบ§18.28(vi) Continuous -Hermite Polynomials
… โบ§18.28(vii) Continuous -Hermite Polynomials
… โบFor continuous -Hermite polynomials the orthogonality measure is not unique. … โบ§18.28(ix) Continuous -Jacobi Polynomials
…19: 32.16 Physical Applications
20: Wolter Groenevelt
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โบGroenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems.
โบAs of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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