Using the functional approach to the theory, Zemanian  has studied $\mathcal A'$-type spaces of generalized functions whose elements may be expanded into series. In  we have studied these spaces (and more general spaces) using the sequential approach similarly as in . An example of this kind of space is the space of generalized functions $L'$ whose elements have Laguerre's expansion into series. In this paper, we study $L'$ space. We indicate that every generalized function from $L'$ represents a tempered distribution observed in the interval $(0,\infty)$. We also indicate that every continuous function of power growth observed in $(0,\infty)$ is a generalized function from $L'$.