Annali di Matematica Pura ed Applicata

, Volume 75, Issue 1, pp 95–120 | Cite as

A class of hypergeometric polynomials

  • Nadhla A. Al-Salam
Article

Summary

In this paper we study the properties of the polynomials\(_3 F_2 \left[ {\begin{array}{*{20}c} { - n,n + \gamma + 1,\zeta ;x} \\ {1 + \alpha ,1 + \beta } \\ \end{array} } \right]\).

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References

  1. [1]
    Nadhla A. Al-Salam,Orthogonal polynomials of hypergeometric type, « Duke Mathematical Journal », Vol. 33 (1966), pp. 109–121.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    W. A, Al-Salam,Operational representation for the Laguerre and other polynomials, « Duke Mathematical Journal », vol. 31 (1964), pp. 127–142.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    E. W. Barnes,A transformation of generalized hypergeometric series, « Quarterly Journal of Mathematics », vol. 41 (1910), pp. 136–140.MATHGoogle Scholar
  4. [4]
    H. Bateman,Some properties of a certain set of polynomials, « The Tohoku Mathematical Journal », vol. 37 (1933), pp. 23–38.MATHGoogle Scholar
  5. [5]
    —— —— The polynomialF n(x), « Annals of Mathematics », vol. 35 (1934), pp. 767–775.CrossRefMATHMathSciNetGoogle Scholar
  6. [6]
    H. Buchholtz, Die Konfluente hypergeometrische Funktionen, Berlin, 1953.Google Scholar
  7. [7]
    L. Carlitz,Bernoulli and Euler numbers and orthogonal polynomials, « Duke Mathematical Journal », vol. 26 (1959), pp. 1–16.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    A. Erdelyi et al, Higher Transcendental Functions, vol. 2,McGraw-Hill Co., New York; 1953.Google Scholar
  9. [9]
    W. Hahn,Uber orthogonal Polynome, die q—Differenzengceichungen genugen, « Mathematische Nachrichten », vol. 2 (1949), pp. 4–34.MATHMathSciNetGoogle Scholar
  10. [10]
    S. Karlin andG. Szegö,On certain determinants whose elements are orthogonal polynomials, « Journal d’Analyse Mathematique », vol. 8 (1960–61), pp. 1–157.MathSciNetCrossRefGoogle Scholar
  11. [11]
    S. Karlin andJ. L. McGregor,The Hahn polynomials, formulas and an application, « Scripta Mathematica », vol. 26 (1961), pp. 33–46.MathSciNetMATHGoogle Scholar
  12. [12]
    S. Pasternack,A generalization of the polynomial F n(x), « Philosophical Magazine and Journal of Science », Ser. 7, vol. 28 (1939), pp. 209–226.MATHMathSciNetGoogle Scholar
  13. [13]
    E. D. Rainville, Special Functions, TheMacmillan Co., New York, 1960.MATHGoogle Scholar
  14. [14]
    —— ——,The contiguous function relations for p F q with application to Bateman’s J n u,v and Rice’s H n (, p, v), « Bulletin of the American Mathematical Society », vol. 51 (1945), pp. 714–723.MATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    S. O. Rice,Some properties of 2 F 3 (−n, n−1, ; 1,p;v), « Duke Mathematical Journal », vol. 6 (1940), pp. 108–119.CrossRefMATHMathSciNetGoogle Scholar
  16. [16]
    R. L. Shively,On Pseudo-Laguerr Polynomials, « University of Michigan thesis », 1953.Google Scholar
  17. [17]
    J. Shohat,Sur les polynomes orthogonaux generalises, « Comptes Rendus », Paris, vol. 207 (1938), p. 556.MATHGoogle Scholar
  18. [18]
    I. N. Sneddon, Fourier Transforms,McGraw Hill Co., New York, 1951.Google Scholar
  19. [19]
    G. Szego,Orthogonal Polynomials, « American Mathematical Society Colloquim Publications », no. 23, revised edition, New York, 1959.Google Scholar
  20. [20]
    M. Weber andA. Erdélyi,On the finite difference analogue of Rodrique’s formula, « American Mathematical Monthly », vol. 59 (1950), pp. 163–168.CrossRefGoogle Scholar
  21. [21]
    E. T. Whittaker andG. N. Watson,A Course of Modern Analysis, « Fourth Edition », Cambridge, 1950.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1967

Authors and Affiliations

  • Nadhla A. Al-Salam
    • 1
  1. 1.EdmontonCanada

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