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Summary

Description

Divergence of the asymptotic series for the w:Exponential integral

The function

gives the first N terms of an approximation to for .

The relative error

is plotted versus for for various numbers of terms, N, as follows:
(red),
(green),
(yellow),
(blue),
(pink).

The larger is, the more terms in this expansion can be taken into account for approximation of the function (and the better the resulting approximation is).
Date
Source Own work
Author Domitori
Permission
(Reusing this file)
Use it please. It is free. The first formula is smooth, you can expand it and do what you like. Enjoy!

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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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Date/TimeThumbnailDimensionsUserComment
current11:30, 4 February 2008Thumbnail for version as of 11:30, 4 February 20081,110 × 1,110 (49 KB)Domitori{{Information |Description=Divergence of the asymptotic series for the w:Exponential integral :<math>{\rm E}_1(z) = \int_1^\infty \frac{e^{-tz}}{t}\, dt,\qquad \Re(z) \ge 0~~.</math> The fincitons :<math> E_1(z,N)= \frac{\exp(-z)}{z} \sum_{n=0}^{N-1

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