ON A GENERALIZED FORMULA OF TAYLOR–MACLAURIN TYPE ON THE GENERALIZED COMPLETELY MONOTONE FUNCTIONS

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ON A GENERALIZED FORMULA OF TAYLOR–MACLAURIN TYPE ON THE GENERALIZED COMPLETELY MONOTONE FUNCTIONS Sahakyan Sahakyan

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.

DOI: 10.46991/PYSU:A/2018.52.3.172 Physical and Mathematical Sciences, 52(3 (247) 172-179

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Keywords

Riemann–Liouville type operators,〈ρj〉completely monotonefunctions.

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