GENERAL ORDER MULTIVARIATE PADE APPROXIMANTS FOR PSEUDO-MULTIVARIATE FUNCTIONS. II

Explicit formulas for general order multivariate Pade approximants of pseudo-multivariate functions are constructed on specific index sets. Examples include the multivariate forms of the exponential function E((x) under bar) = Sigma(infinity)(ji,j2,...,jm=0) x(1)(j1)x(2)(j2) ... x(m)(jm)/(j(1) + j(2) +...+ j(m))!' the logarithm function L((x) under bar) = Sigma(j1+j2+...+jm >= 1) x(1)(j1)x(2)(j2) ... x(m)(jm)/j(1) + j(2) +...+ j(m), the Lauricella function F(D)((m)) (a,1,...,1;c;x(1),...,x(m)) = Sigma(infinity)(j1,j2,...,jm=0) (a)(j1+...+jm)/(c)(j1+...+jm) x(1)(j1)...x(m)(jm), and many more. We prove that the constructed approximants inherit the normality and consistency properties of their univariate relatives. These properties do not hold in general for multivariate Pade approximants. A truncation error upperbound is also given.