Numerical Algorithms

, 49:159 | Cite as

Evaluation of q-gamma function and q-analogues by iterative algorithms

  • Bruno Gabutti
  • Giampietro Allasia
Original Paper


Two known two-dimensional algorithms, obtained by modifying the classical arithmetic-harmonic mean, are reconsidered. Some rapidly convergent sequences associated with the algorithms are established and applied to the evaluation of q-analogous functions. Computation of q-gamma function, q-beta function, and q-exponential function is shown to be effective.


Two-term recurrence relations Infinite products Convergence rate q-gamma function 

Mathematics Subject Classifications (2000)

65D20 33D05 


  1. 1.
    Allasia, G., Bonardo, F.: On the numerical evaluation of two infinite products. Math. Comp. 35(151), 917–931 (1980)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Andrews, G.E., Askey, R., Roy, R.: Special Functions. Encyclopedia of Mathematics and Its Applications, vol. 71. Cambridge Univ. Press, Cambridge (2004)Google Scholar
  3. 3.
    Borwein, J.M., Borwein, P.B.: Pi and the AGM. A Study in Analytic Number Theory and Computational Complexity. Wiley, New York (1987)MATHGoogle Scholar
  4. 4.
    Forster, D.M.E., Phillips, G.M.: The arithmetic-harmonic mean. Math. Comp. 42, 83–91 (1984)Google Scholar
  5. 5.
    Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyclopedia of Mathematics and its Applications, vol. 35. Cambridge Univ. Press, Cambridge (1990)Google Scholar
  6. 6.
    Gatteschi, L.: Procedimenti iterativi per il calcolo numerico di due prodotti infiniti. Rend. Sem. Mat. Univ. Politec. Torino 29, 187–201 (1969–70)MathSciNetGoogle Scholar
  7. 7.
    Gautschi, W.: Luigi Gatteschi’s work on special functions and numerical analysis. In: Allasia, G. (ed.) Special Functions. Ann. Numer. Math. 2(1–4), pp. 3–19 (1995)Google Scholar
  8. 8.
    Slater, L.J.: Some new results on equivalent products. Proc. Cambridge Phil. Soc. 50, 394–403 (1954)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Wimp, J.: Computation with Recurrence Relations. Pitman, London (1984)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TurinTurinItaly

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