In the paper Taylor–Maclaurin type formulas for some classes of functionsare obtained. The main result of this study introduces an idea of the generalizedclasses of〈ρj〉completely monotone function. Under the various conditions
(∞∑j=11ρj<+∞,∞∑j=11ρj= +∞,)
the terms of their representation are obtainedand some related theorems are proved.