Explicit Construction of Multivariate Padé Approximants for a q-Logarithm Function Original Research Article

We explicitly construct the non-homogeneous multivariate Padé approximants to a two variable version of the q-logarithm functionLq(x, y)≔∑i, j=0∞ (q−1) xiyjqi+j+1−1, for |q|>1 and |x|, |y|<|q|, by using the residue theorem and functional equation method.