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Integrated Journal for Research in Arts and Humanities
Article . 2022 . Peer-reviewed
License: CC BY NC ND
Data sources: Crossref
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Harmonic Mean and Contra-Harmonic Mean Derivative-Based Closed Newton-Cotes Quadrature

descriptionPublicationkeyboard_double_arrow_right Article 31 May 2022Publisher:Stallion PublicationJournal:Integrated Journal for Research in Arts and Humanities, volume 2, pages 55-61 (eissn: 2583-1712, Copyright policy )
Authors: null Kaushal Rana;

doi: 10.55544/ijrah.2.3.36

Harmonic Mean and Contra-Harmonic Mean Derivative-Based Closed Newton-Cotes Quadrature

Abstract

In this paper, the Harmonic mean and Contra-harmonic mean of two endpoints [a,b] are applied at the derivative of the error term in the existing CNC formulas. This modified error term is included as an additional function to the existing formula. The new error terms are derived using the method of precision for the proposed formulas. Comparisons are made between the existing CNC formulas and the proposed CNC formulas by using numerical examples. The proposed Harmonic mean derivate-based (HMD) and the Contra-harmonic mean derivative-based (CHMD). CNC formulas give better results for definite integrals. Another two of its statistical means are discussed and derived for the existing CNC formulas in the subsequent paper.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Average
Top 10%
gold