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representation as q-hypergeometric functions

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1: 18.28 Askey–Wilson Class
For ω y and h n see Koekoek et al. (2010, Eq. (14.2.2)).
2: 17.6 ϕ 1 2 Function
§17.6(v) Integral Representations
3: 17.7 Special Cases of Higher ϕ s r Functions
Sum Related to (17.6.4)
q -Pfaff–Saalschütz Sum
Nonterminating Form of the q -Saalschütz Sum
Continued Fractions
For continued-fraction representations of a ratio of ϕ 2 3 functions, see Cuyt et al. (2008, pp. 399–400). …
4: 18.27 q -Hahn Class
They are defined by their q -hypergeometric representations, followed by their orthogonality properties. …
§18.27(ii) q -Hahn Polynomials
§18.27(iii) Big q -Jacobi Polynomials
§18.27(iv) Little q -Jacobi Polynomials
Discrete q -Hermite II
5: Bibliography Z
  • A. Zarzo, J. S. Dehesa, and R. J. Yañez (1995) Distribution of zeros of Gauss and Kummer hypergeometric functions. A semiclassical approach. Ann. Numer. Math. 2 (1-4), pp. 457–472.
  • D. Zeilberger and D. M. Bressoud (1985) A proof of Andrews’ q -Dyson conjecture. Discrete Math. 54 (2), pp. 201–224.
  • Zeilberger (website) Doron Zeilberger’s Maple Packages and Programs Department of Mathematics, Rutgers University, New Jersey.
  • Q. Zheng (1997) Generalized Watson Transforms and Applications to Group Representations. Ph.D. Thesis, University of Vermont, Burlington,VT.
  • M. I. Žurina and L. N. Osipova (1964) Tablitsy vyrozhdennoi gipergeometricheskoi funktsii. Vyčisl. Centr Akad. Nauk SSSR, Moscow (Russian).
  • 6: Bibliography R
  • W. H. Reid (1995) Integral representations for products of Airy functions. Z. Angew. Math. Phys. 46 (2), pp. 159–170.
  • W. H. Reid (1997a) Integral representations for products of Airy functions. II. Cubic products. Z. Angew. Math. Phys. 48 (4), pp. 646–655.
  • W. H. Reid (1997b) Integral representations for products of Airy functions. III. Quartic products. Z. Angew. Math. Phys. 48 (4), pp. 656–664.
  • RISC Combinatorics Group (website) Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.
  • Hans-J. Runckel (1971) On the zeros of the hypergeometric function. Math. Ann. 191 (1), pp. 53–58.