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

Abstract

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.

On a connection between formulas about q–gamma functions

“…Its properties and different representations were discussed in numerous papers, such as in [4], [12] and [11]. A few successful algorithms for its numerical evaluation are introduced in [7] and [6] and [1]. An asymptotic expansion of the q-gamma function was provided in [3].…”

Biographic notes on Luigi Gatteschi

“…Nevertheless, he kept his mind engaged in research until the very last moments of his life (see e.g. [13] and the note to [14]). Mathematics has really represented for Luigi a fundamental value, a passionate love, and a reason of life.…”