Integration by Parts and Infinite Series

به سوی علوم ریاضی

Article 1, Volume 3, Issue 1 - Serial Number 3, October 2023, Pages 1-8   

Document Type: Translation

DOI: 10.22067/tmsj.2023.43621

Authors

Amirmohamamd Momeni kohestani^{* 1}; Alireza Khalili Asboei²

¹Bachelor of Mathematics Education, Farhangian University, Tehran, Iran

²Department of Mathematics, Farhangian University, Tehran, Iran

Abstract

In this paper, by using a student’s calculation error in applying the integration formula using the subtraction method and reaching the correct answer, we reached the following formula ∫ fg = Σ1 k=0(-1)kf(k)g-(k+1) where g-(k) is the k th successive antiderivative of g and f(k) is the k th derivative of ffi. We find by using the above series and Maclaurin series, interesting results about the convergence of some series. Also, due to the introductory nature of the integration formula using the subtraction and the infinite series, this series can be new topics for the next research is to provide researchers with a new method for deriving series and discovering new series.

Keywords

Frames; dual frames; optimal duals; reconstruction formulas

References