Explicit construction of multivariate Padé approximants for a \(q\)-logarithm function (Q1971643)

This paper is concerned with the explicit construction of the nonhomogeneous multivariate Padé approximants to a two variable version of a \(q\)-logarithm function \[ L_q(x,y)= \sum^\infty_{i,j =0}{(q-1) x^iy^i \over q^{i+j+1} -1}, \] for \(|q|>1\) and \(|x|, |y|<|q |\). The residue theorem and the functional equation method, introduced earlier by the author [J. Comput. Appl. Math. 79, No. 1, 1-17 (1997; Zbl 0865.41018); J. Approximation Theory 93, No. 2, 201-300 (1998; Zbl 0903.41007)], are used.