Monatshefte für Mathematik

, Volume 88, Issue 2, pp 87–105

Operatormethoden fürq-Identitäten

  • J. Cigler

Operator methods forq-identities


We use some simple operator methods in order to give more insight intoq-identities.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Al-Salam, W. A., undM. E. H. Ismail: Some operational formulas. J. Math. Anal. Appl.51, 208–218 (1975).Google Scholar
  2. [2]
    Carlitz, L.:q-Bernoulli numbers and polynomials. Duke Math. J.15, 987–1000 (1948).Google Scholar
  3. [3]
    Carlitz, L.: Aq-identity. Mh. Math.67, 305–310 (1963).Google Scholar
  4. [4]
    Cigler, J.: Some remarks on Rota's umbral calculus. Indag. Math.40, 27–42 (1978).Google Scholar
  5. [5]
    Feinsilver, Ph. J.: Special Functions, Probability Semigroups, and Harmonic Flows. Lecture Notes Math. 696. Berlin-Heidelberg-New York: Springer. 1978.Google Scholar
  6. [6]
    Goldman, J., undG.-C. Rota: Finite vector spaces and Eulerian generating functions. Studies Appl. Math.49, 239–258 (1970).Google Scholar
  7. [7]
    Gould, H. W.: Theq-Stirling numbers of first and second kinds. Duke Math. J.28, 281–289 (1961).Google Scholar
  8. [8]
    Gould, H. W., undA. T. Hopper: Operational formulas connected with two generalizations of Hermite polynomials. Duke Math. J.29, 51–63 (1962).Google Scholar
  9. [9]
    Hirschhorn, M. D.: Simple proofs of identities of MacMahon und Jacobi. Discrete Math.16, 161–162 (1976).Google Scholar
  10. [10]
    Kirschenhofer, P.: Beiträge zu Rota's Theorie der Sheffer- und Faktorfolgen. Dissertation. Wien. 1979.Google Scholar
  11. [11]
    Klamkin, M. S., undD. J. Newman: On the reducibility of some linear differential operators. Amer. Math. Monthly,66, 293–295 (1959).Google Scholar
  12. [12]
    Riordan, J.: Combinatorial Identities. New York-London: J. Wiley. 1968.Google Scholar
  13. [13]
    Roman, S. M., undG.-C. Rota: The umbral calculus. Adv. Math.27, 95–188 (1978).Google Scholar
  14. [14]
    Rota, G.-C., D. Kahaner undA. Odlyzko: Finite operator calculus. J. Math. Anal. Appl.42, 684–760 (1973).Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • J. Cigler
    • 1
  1. 1.Institut für MathematikUniversität WienWienÖsterreich

Personalised recommendations