In this paper we present a general methodology to obtain a generating function for some multiple orthogonal polynomials of type I with regular indices. In particular, we obtain an explicit generating functions Px(t): = ∑n=0∞ Q2n(x)tn and Ix(t): = ∑n=0∞ Q2n+1(x)tn with Qn(x) = qn,1(x) + x qn,2(x) where (qn,1(x), qn,2(x)) is the r-vector of type I associated with the multiple orthogonal Hermite polynomial with regular index for r = 2.
