Editing Exponential integral (section)

===Exponential and logarithmic behavior: bracketing===
[[Image:BracketingE1.png|right|200px|thumb|Bracketing of <math>E_1</math> by elementary functions]]

From the two series suggested in previous subsections, it follows that <math>E_1</math> behaves like a negative exponential for large values of the argument and like a logarithm for small values. For positive real values of the argument, <math>E_1</math> can be bracketed by elementary functions as follows:<ref>Abramowitz and Stegun, p.&nbsp;229, 5.1.20</ref>
:<math>
\frac 1 2 e^{-x}\,\ln\!\left( 1+\frac 2 x \right)
< E_1(x) < e^{-x}\,\ln\!\left( 1+\frac 1 x \right)
\qquad x>0
</math>

The left-hand side of this inequality is shown in the graph to the left in blue; the central part <math>E_1(x)</math> is shown in black and the right-hand side is shown in red.