Andrews–Askey sum
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1—10 of 12 matching pages
1: 17.6 Function
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Andrews–Askey Sum
…2: 17.7 Special Cases of Higher Functions
3: Richard A. Askey
Profile
Richard A. Askey
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βΊRichard A. Askey (b.
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βΊ Andrews and R.
…Another significant contribution was the Askey-Gasper inequality for Jacobi polynomials which was published in Positive Jacobi polynomial sums. II (with G.
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βΊ Andrews, B.
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4: Bibliography
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Ramanujan Revisited.
Academic Press Inc., Boston, MA.
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Special Functions.
Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, Cambridge.
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Classical Orthogonal Polynomials.
In Orthogonal Polynomials and Applications, C. Brezinski, A. Draux, A. P. Magnus, P. Maroni, and A. Ronveaux (Eds.),
Lecture Notes in Math., Vol. 1171, pp. 36–62.
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Positive Jacobi polynomial sums. II.
Amer. J. Math. 98 (3), pp. 709–737.
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Some basic hypergeometric extensions of integrals of Selberg and Andrews.
SIAM J. Math. Anal. 11 (6), pp. 938–951.
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5: 18.18 Sums
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βΊSee Andrews et al. (1999, Lemma 7.1.1) for the more general expansion of in terms of .
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§18.18(vi) Bateman-Type Sums
βΊJacobi
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… βΊ6: 18.38 Mathematical Applications
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βΊThe Askey–Gasper inequality
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βΊSee, for example, Andrews et al. (1999, Chapter 9).
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βΊSee Zhedanov (1991), GranovskiΔ et al. (1992, §3), Koornwinder (2007a, §2) and Terwilliger (2011).
Similar algebras can be associated with all families of OP’s in the -Askey scheme and the Askey scheme.
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βΊDunkl type operators and nonsymmetric polynomials have been associated with various other families in the Askey scheme and -Askey scheme, in particular with Wilson polynomials, see Groenevelt (2007), and with Jacobi polynomials, see Koornwinder and Bouzeffour (2011, §7).
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7: Bibliography G
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The GAP Group, Centre for Interdisciplinary Research in Computational Algebra,
University of St. Andrews, United Kingdom.
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Basic Hypergeometric Series.
Second edition, Encyclopedia of Mathematics and its Applications, Vol. 96, Cambridge University Press, Cambridge.
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Computational Methods in Special Functions – A Survey.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975), R. A. Askey (Ed.),
pp. 1–98. Math. Res. Center, Univ. Wisconsin Publ., No. 35.
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Applications of the classical umbral calculus.
Algebra Universalis 49 (4), pp. 397–434.
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Representations of Integers as Sums of Squares.
Springer-Verlag, New York.
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8: 14.30 Spherical and Spheroidal Harmonics
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βΊSee also (34.3.22), and for further related integrals see Askey et al. (1986).
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14.30.8_5
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§14.30(iii) Sums
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14.30.9
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βΊSee Andrews et al. (1999, Chapter 9).
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9: 18.27 -Hahn Class
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βΊThe
-hypergeometric OP’s comprise the -Hahn class (or -linear lattice class) OP’s and the Askey–Wilson class (or -quadratic lattice class) OP’s (§18.28).
Together they form the
-Askey scheme.
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18.27.2
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18.27.6
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18.27.12_5
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10: Bibliography M
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Associated Wilson polynomials.
Constr. Approx. 7 (4), pp. 521–534.
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On a class of algebraic solutions to the Painlevé VI equation, its determinant formula and coalescence cascade.
Funkcial. Ekvac. 46 (1), pp. 121–171.
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A new symmetry related to for classical basic hypergeometric series.
Adv. in Math. 57 (1), pp. 71–90.
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Analytic Inequalities.
Springer-Verlag, New York.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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