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relation to q-hypergeometric functions

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1: 18.27 q -Hahn Class
§18.27(ii) q -Hahn Polynomials
§18.27(iii) Big q -Jacobi Polynomials
§18.27(iv) Little q -Jacobi Polynomials
§18.27(v) q -Laguerre Polynomials
Discrete q -Hermite II
2: 18.28 Askey–Wilson Class
§18.28(ii) Askey–Wilson Polynomials
§18.28(viii) q -Racah Polynomials
For ω y and h n see Koekoek et al. (2010, Eq. (14.2.2)).
3: 17.8 Special Cases of ψ r r Functions
Ramanujan’s ψ 1 1 Summation
Quintuple Product Identity
Bailey’s Bilateral Summations
Sum Related to (17.6.4)
For similar formulas see Verma and Jain (1983).
4: 17.7 Special Cases of Higher ϕ s r Functions
Sum Related to (17.6.4)
5: George E. Andrews
An expert on q -series, he is the author of q -Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. … Andrews was elected to the American Academy of Arts and Sciences in 1997, and to the National Academy of Sciences (USA) in 2003. …Andrews served as President of the AMS from February 1, 2009 to January 31, 2011, and became a Fellow of the AMS in 2012. …
  • 6: 17.13 Integrals
    §17.13 Integrals
    In this section, for the function Γ q see §5.18(ii). …or, when 0 < q < 1 , …
    Ramanujan’s Integrals
    Askey (1980) conjectured extensions of the foregoing integrals that are closely related to Macdonald (1982). …
    7: Bibliography Z
  • F. A. Zafiropoulos, T. N. Grapsa, O. Ragos, and M. N. Vrahatis (1996) On the Computation of Zeros of Bessel and Bessel-related Functions. In Proceedings of the Sixth International Colloquium on Differential Equations (Plovdiv, Bulgaria, 1995), D. Bainov (Ed.), Utrecht, pp. 409–416.
  • D. Zagier (1989) The Dilogarithm Function in Geometry and Number Theory. In Number Theory and Related Topics (Bombay, 1988), R. Askey and others (Eds.), Tata Inst. Fund. Res. Stud. Math., Vol. 12, pp. 231–249.
  • 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.
  • 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.
  • 8: 18.33 Polynomials Orthogonal on the Unit Circle
    §18.33(ii) Recurrence Relations
    Let { p n ( x ) } and { q n ( x ) } , n = 0 , 1 , , be OP’s with weight functions w 1 ( x ) and w 2 ( x ) , respectively, on ( - 1 , 1 ) . …
    Szegő–Askey
    For the hypergeometric function F 1 2 see §§15.1 and 15.2(i). … For the notation, including the basic hypergeometric function ϕ 1 2 , see §§17.2 and 17.4(i). …
    9: Bibliography R
  • D. St. P. Richards (Ed.) (1992) Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications. Contemporary Mathematics, Vol. 138, American Mathematical Society, Providence, RI.
  • D. St. P. Richards (2004) Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.
  • 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.
  • J. Rushchitsky and S. Rushchitska (2000) On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.
  • 10: 17.6 ϕ 1 2 Function
    First q -Chu–Vandermonde Sum
    Andrews–Askey Sum
    Bailey–Daum q -Kummer Sum
    Nonterminating Form of the q -Vandermonde Sum
    Heine’s Contiguous Relations