Let $Q$ be a nonconstant polynomial with integer coefficients and without zeros at the non–negative integers. Essentially with the method of Hermite, a new proof is given on linear independence of values at rational points of the function$$\begin{array}{c}\hfill G\left(x\right)=\sum _{n=0}^{\infty }\frac{x^n}{Q\left(1\right)Q\left(2\right)\cdots Q\left(n\right)}.\end{array}$$