By means of a sequence $\varphi_{\cdot}:= (\varphi_n)_{n\in\mathbb N}$ of square-integrable functions a notion of a $\varphi_{\cdot}$-summing operator is defined. It is shown that if $\inf_n\|\varphi_n\|_2 > 0$, then any $\varphi_{\cdot}$-summing operator is Gaussian-summing. This recovers a previously known result, which asserts the same in case when $\varphi_{\cdot}:= (\varphi_n)_{n\in\mathbb N}$ is an orthonormal sequence.