Numerical Algorithms

, Volume 30, Issue 3–4, pp 323–333 | Cite as

Zeros of \(_3 F_2 (_{d,e}^{ - n,b,c} ;z) \) Polynomials

  • K. Driver
  • K. Jordaan
Article

Abstract

We establish the location of the zeros of several classes of 3F2 hypergeometric polynomials that admit representations as various kinds of products involving 2F1 polynomials. We categorise the 3F2 polynomials considered here according to whether they are well-poised or k-balanced. Our results include and extend those obtained in [5].

zeros of hypergeometric polynomials zeros of \(_3 F_2 (_{d,e}^{ - n,b,c} ;z)\) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).Google Scholar
  2. [2]
    G. Andrews, R. Askey and R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications (Cambridge Univ. Press, Cambridge, 1999).Google Scholar
  3. [3]
    K. Driver and P. Duren, Zeros of the hypergeometric polynomials F(-n, b; 2b; z), Indag. Math. 11(1) (2000) 43–51.Google Scholar
  4. [4]
    K. Driver and P. Duren, Trajectories of the zeros of hypergeometric polynomials F(-n, b; 2b; z) for b < -1/2, Constr. Approx. 17 (2001) 169–179.Google Scholar
  5. [5]
    K. Driver and A. Love, Zeros of 3F2 hypergeometric polynomials, J. Comput. Appl. Math. 131 (2001) 243–251.Google Scholar
  6. [6]
    K. Driver and M. Möller, Zeros of the hypergeometric polynomials F(-n, b;-2n; z), J. Approx. Theory 110 (2001) 74–87.Google Scholar
  7. [7]
    K. Driver and M. Möller, Quadratic and cubic transformations and the zeros of hypergeometric polynomials, J. Comput. Appl. Math. 142(2) (2002) 411–417.Google Scholar
  8. [8]
    F. Klein, Ñber die Nullstellen der hypergeometrischen Reihe, Mathematische Annalen 37 (1890) 573–590.Google Scholar
  9. [9]
    A.P. Prudnikov, Yu.A. Brychkov and O.I. Marichev, Integrals and Series, Vol. 3 (Nauka, Moscow, 1986) (in Russian); English translation (Gordon & Breach, New York, 1988); Errata in Math. Comp. 65 (1996) 1380–1384.Google Scholar
  10. [10]
    G. Szegő, Orthogonal Polynomials (Amer. Math. Soc., New York, 1959).Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • K. Driver
  • K. Jordaan

There are no affiliations available

Personalised recommendations