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

B.A. Sahakyan

doi:10.46991/PYSU:A/2018.52.3.172

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

Authors

B.A. Sahakyan Chair of General Mathematics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2018.52.3.172

Keywords:

Riemann–Liouville type operators, $ \langle \rho_j \rangle $ completely monotone functions

Abstract

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 $ \langle \rho_j \rangle $ completely monotone function. Under the various conditions $ \left( \sum\limits_{j=1}^{\infty} \dfrac{1}{\rho_j} < + \infty ,\ \sum\limits_{j=1}^{\infty} \dfrac{1}{\rho_j} = + \infty \right) $ the terms of their representation are obtained and some related theorems are proved.

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Published

2018-12-17

How to Cite

Sahakyan, B. (2018). ON A GENERALIZED FORMULA OF TAYLOR–MACLAURIN TYPE ON THE GENERALIZED COMPLETELY MONOTONE FUNCTIONS. Proceedings of the YSU A: Physical and Mathematical Sciences, 52(3 (247), 172–179. https://doi.org/10.46991/PYSU:A/2018.52.3.172