General order multivariate Padé approximants for Pseudo-multivariate functions. II

Explicit formulas for general order multivariate Padé approximants of pseudo-multivariate functions are constructed on specific index sets. Examples include the multivariate forms of the exponential function

$$E\left(\underline{x}\right) =\sum_{j_{1},j_{2},\ldots ,j_{m}=0}^{... ...x_{2}^{j_{2}}\cdots x_{m}^{j_{m}}}{\left( j_{1}+j_{2}+\cdots +j_{m}\right) !},$$

the logarithm function

$$L(\underline{x})=\sum_{j_{1}+j_{2}+\cdots +j_{m}\geq 1}\frac{ x_{1}^{j_{1}}x_{2}^{j_{2}}\cdots x_{m}^{j_{m}}}{j_{1}+j_{2}+\cdots +j_{m}},$$

the Lauricella function

$$F_{D}^{\left( m\right) }\left( a,1,\ldots ,1;c;x_{1},\ldots ,x_{m... ...}}}{\left( c\right) _{j_{1}+\cdots +j_{m}}} x_{1}^{j_{1}}\cdots x_{m}^{j_{m}},$$

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 Padé approximants. A truncation error upperbound is also given.