representation as q-hypergeometric functions
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1: 18.28 Askey–Wilson Class
2: 17.6 Function
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§17.6(v) Integral Representations
…3: 17.7 Special Cases of Higher Functions
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Sum Related to (17.6.4)
… ►-Pfaff–Saalschütz Sum
… ►Nonterminating Form of the -Saalschütz Sum
… ►Continued Fractions
►For continued-fraction representations of a ratio of functions, see Cuyt et al. (2008, pp. 399–400). …4: 18.27 -Hahn Class
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►They are defined by their -hypergeometric representations, followed by their orthogonality properties.
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§18.27(ii) -Hahn Polynomials
… ►§18.27(iii) Big -Jacobi Polynomials
… ►§18.27(iv) Little -Jacobi Polynomials
… ►Discrete -Hermite II
…5: Bibliography Z
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Distribution of zeros of Gauss and Kummer hypergeometric functions. A semiclassical approach.
Ann. Numer. Math. 2 (1-4), pp. 457–472.
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A proof of Andrews’ -Dyson conjecture.
Discrete Math. 54 (2), pp. 201–224.
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Doron Zeilberger’s Maple Packages and Programs
Department of Mathematics, Rutgers University, New Jersey.
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Generalized Watson Transforms and Applications to Group Representations.
Ph.D. Thesis, University of Vermont, Burlington,VT.
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Tablitsy vyrozhdennoi gipergeometricheskoi funktsii.
Vyčisl. Centr Akad. Nauk SSSR, Moscow (Russian).
6: Bibliography R
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Integral representations for products of Airy functions.
Z. Angew. Math. Phys. 46 (2), pp. 159–170.
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Integral representations for products of Airy functions. II. Cubic products.
Z. Angew. Math. Phys. 48 (4), pp. 646–655.
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Integral representations for products of Airy functions. III. Quartic products.
Z. Angew. Math. Phys. 48 (4), pp. 656–664.
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Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.
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On the zeros of the hypergeometric function.
Math. Ann. 191 (1), pp. 53–58.
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