The authors nicely explores a multivariable generalization of famous two-variable Lagrangian polynomials \(g^{(\alpha,\beta)}_n(x,y)\). The said generalization has its explicit representation given by \[ g^{(\alpha_1,\dots,\alpha_r)}_n(x_1,\dots, x_r)= \sum_{k_1+\cdots+ k_r= n} (\alpha_1)_{k_1}\cdots (\alpha_r)_{k_r} {x^{k_1}_1\over k_1!}\cdots {x^{k_r}_r\over k_r!} \] being Pochhammer symbol. The authors use tested series-manipulation technique to deliver here also a multilinear and a multilateral generating function and a recursion relation. The polynomials need to be examined for their other properties such as expansion-problems and of course Rodrigues type of formula.