2018; Physical and Mathematical Sciences, 52(3 (247): 172–179
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ON A GENERALIZED FORMULA OF TAYLOR–MACLAURIN TYPE ON THE GENERALIZED COMPLETELY MONOTONE FUNCTIONS

Sahakyan Sahakyan*

Received: 2025-01-30 · Published: 2018-12-17

© 2018 The Author(s) and the original publisher.

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Original title
ON A GENERALIZED FORMULA OF TAYLOR–MACLAURIN TYPE ON THE GENERALIZED COMPLETELY MONOTONE FUNCTIONS
Author
Sahakyan Sahakyan
Published
2018-12-17
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2018.52.3.172

Abstract

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.
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