Estimating Sums of Convergent Series via Rational Polynomials  

作　　者：Serdar Beji Serdar Beji(Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Turkey)

机构地区：[1]Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Turkey

出　　处：《Advances in Pure Mathematics》2023年第4期187-197,共11页理论数学进展（英文）

摘　　要：Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with second-degree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with second-degree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.

关 键 词：Sums of Series Rational Polynomials Extrapolation to Limit Asymptotic Value 

分 类 号：O17[理学—数学]