ON A GENERALIZED FORMULA OF TAYLOR–MACLAURIN TYPE ON THE GENERALIZED COMPLETELY MONOTONE FUNCTIONS - Sahakyan, B.A. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2018)
In the paper Taylor–Maclaurin type formulas for some classes of functions are obtained. The main result of this study introduces an idea of the generalized classes of ρ_j completely monotone function. Under the various conditions ( _j=1^∞ 1ρ_j < + ∞ , _j=1^∞ 1ρ_j = + ∞ ) the terms of their representation are obtained and some related theorems are proved.