关于广义完全单调函数的泰勒-麦克劳林型的一个广义公式

Proceedings of the YSU A: Physical and Mathematical Sciences Pub Date : 2018-12-17 DOI:10.46991/pysu:a/2018.52.3.172

B. A. Sahakyan

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引用次数: 0

摘要

本文给出了一类函数的泰勒-麦克劳林型公式。本研究的主要结果引入了$ \langle \rho_j \rangle $全单调函数广义类的思想。在各种条件下$ \left( \sum\limits_{j=1}^{\infty} \dfrac{1}{\rho_j} < + \infty ,\ \sum\limits_{j=1}^{\infty} \dfrac{1}{\rho_j} = + \infty \right) $得到了它们的表示形式，并证明了一些相关定理。

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

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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Proceedings of the YSU A: Physical and Mathematical Sciences

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