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Evaluation of $q$-gamma function and $q$-analogues by iterative algorithms. (English) Zbl 1162.65008
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:
 65D20 Computation of special functions, construction of tables 33D05 $q$-gamma functions, $q$-beta functions and integrals 33F05 Numerical approximation and evaluation of special functions
##### References:
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