Document Type
Conference Proceeding
Publication Date
5-29-2009
Abstract
The Euler-Maclaurin summation formula is frequently used to efficiently estimate sums of infinite series of the form $\sum_{j=1}^{\infty}f(j)$. The purpose of this article is to describe a modification of this numerical technique designed to simplify and reduce the computational effort required to obtain an acceptable estimate of the sum. The modified formula is obtained by replacing $f\left( x\right) $ with an easily constructed polynomial like interpolating function $a\left( x\right) $ designed to simplify the calculation of the integral and derivatives associated with Euler-Maclaurin. This approach provides a more tractable algorithm which can be written as a matrix equation. Examples are provided to demonstrate that the accuracy of the new algorithm compares favorably with that of the traditional formula. The paper concludes with a brief discussion of a method for approximating the error incurred when replacing the exact value of the sum of the original series with the estimate.
Recommended Citation
Garrison, Kara and Price, Thomas E., "Approximating Sums of Infinite Series" (2009). ACMS Conference Proceedings 2009. 17.
https://pillars.taylor.edu/acms-2009/17
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