Explicit computation of Padé-Hermite approximants (Q1352918)

The diagonal Padé-Hermite approximants to a system of functions connected with the \(q\)-logarithm \(L_q(x) = \sum {x^n \over (q^n-1)}\) are explicitly computed using the Siegel method (differentiation of considered functions to obtain a recurrence relation and next the establishment of a multiple integral formulae for polynomials) commuted to the \(q\)-derivation replacing the ordinary derivation. Such approximants are very useful in number theory.