ESTIMATING THE REMAINDER OF AN ALTERNATING p–SERIES USING HYPERGEOMETRIC FUNCTIONS

Othman Echi; Adel Khalfallah; Dhaker Kroumi

doi:10.7153/jmi-2023-17-36

ESTIMATING THE REMAINDER OF AN ALTERNATING p–SERIES USING HYPERGEOMETRIC FUNCTIONS

Othman Echi^*, Adel Khalfallah, Dhaker Kroumi

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, using hypergeometric functions, we provide sharp estimates of the remainder of the alternating p-series,(Formula Presented)is an integer. We show that the largest ρ and the largest σ such that the inequalities (Formula Presented)hold for any integer(Formula Presented)(Formula Presented)the Riemann zeta function.

Original language	English
Pages (from-to)	569-580
Number of pages	12
Journal	Journal of Mathematical Inequalities
Volume	17
Issue number	2
DOIs	https://doi.org/10.7153/jmi-2023-17-36
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023, Element D.O.O.. All Rights Reserved.

Keywords

Alternating series
estimate of the remainder of a series
hypergeometric series

ASJC Scopus subject areas

Analysis

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10.7153/jmi-2023-17-36

Cite this

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abstract = "In this paper, using hypergeometric functions, we provide sharp estimates of the remainder of the alternating p-series,(Formula Presented)is an integer. We show that the largest ρ and the largest σ such that the inequalities (Formula Presented)hold for any integer(Formula Presented)(Formula Presented)the Riemann zeta function.",

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KW - Alternating series

KW - estimate of the remainder of a series

KW - hypergeometric series

UR - https://www.scopus.com/pages/publications/85167876339

U2 - 10.7153/jmi-2023-17-36

DO - 10.7153/jmi-2023-17-36

M3 - Article

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JO - Journal of Mathematical Inequalities

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ER -

ESTIMATING THE REMAINDER OF AN ALTERNATING p–SERIES USING HYPERGEOMETRIC FUNCTIONS

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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