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There is a trend to moving from

LaTeX Math Inline

body	\rm Ei

definition which was dominating in the past towards

LaTeX Math Inline

body	\rm E_1

.

For the small arguments Approximations:

LaTeX Math Inline

body	\|x\| \ll 1

LaTeX Math Inline

body	\|x\| \gg 1

LaTeX Math Block

anchor	2
alignment	left

{\rm Ei}(x) = \gamma + \ln |x| + \sum_{k=1

...

}^\infty \frac{x^k}{k\cdot k!}

LaTeX Math Block

anchor	2
alignment	left

{\rm Ei}(x) = e^x \, \left[ \frac{1}{x} + \sum_{k=2}^\infty \frac{(k-1)!}{x^k} \right]

LaTeX Math Inline

body	-1 \ll x <0

LaTeX Math Inline

body	0 < x \ll 1

LaTeX Math Block

anchor	2
alignment	left

{\rm Ei}(x) = -\gamma - \ln (-x)

LaTeX Math Block

anchor	2
alignment	left

{\rm Ei}(x) = \gamma + \ln x

where

LaTeX Math Inline

body	\gamma = 0.577 ...

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