The Generation of Diagonal Bivariate Quadratic Padé Approximation

The generation of successive diagonal quadratic approximants f_m/_m/_m(x; y) of a bivariate function f(x; y) which has a formal power series expansion about the origin is discussed. A necessary and sufficient condition for the non-degeneracy of f_m/_m/_m(x; y) is given. The computational scheme extends to cover the computation of diagonal quadratic approximants in N variables.