Adapted multivariate Padé approximation (Q435990)

The authors introduce a new strategy to calculate a multivariate Padé approximant that is adapted for the class of functions which are written in the form NEWLINE\[NEWLINEu(x,y)=\sum_{l=1}^{N}P_{l}(x,y)g_{l}(\varphi _{l}(x,y))NEWLINE\]NEWLINE where \( P_{l}(x,y)\) is a polynomial, \(\varphi(x,y)\) is a known function and \(g_{l}\) is a function given by its Taylor series expansion. The definition presented in the paper is designed to avoid disadvantages of the definitions of homogeneous Padé approximation and general Padé approximation. The main result obtained as consequence of this definition is some convergence results of multivariate Stieltjes series and a generalization of the Montessus De Ballore theorem for this class of multivariate functions.