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Zbl 1162.65008
Gabutti, Bruno; Allasia, Giampietro
Evaluation of $q$-gamma function and $q$-analogues by iterative algorithms. (English)
[J] Numer. Algorithms 49, No. 1-4, 159-168 (2008). ISSN 1017-1398; ISSN 1572-9265/e

Summary: 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.

MSC 2000:: *65D20 Computation of special functions
33D05 q-gamma functions, q-beta functions and integrals
33F05 Numerical approximation of special functions

Keywords: two-term recurrence relations; infinite products; convergence rate; $q$-gamma function; numerical examples; algorithms; $q$-beta function; $q$-exponential function

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