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simplify/Ei

simplify expressions involving Exponential Integrals

 Calling Sequence simplify(expr, Ei)

Parameters

 expr - any expression Ei - literal name; Ei

Description

 • The simplify/Ei function is used to simplify expressions involving exponential integrals by applying the identities

$\mathrm{Ei}\left(1,Ix\right)+\mathrm{Ei}\left(1,-Ix\right)\to -2\mathrm{Ci}\left(x\right)+\left(\mathrm{csgn}\left(x\right)-1\right)I\mathrm{Pi}$

$\mathrm{Ei}\left(1,Ix\right)-\mathrm{Ei}\left(1,-Ix\right)\to 2I\mathrm{Si}\left(x\right)-I\mathrm{Pi}\mathrm{csgn}\left(x\right)$

Examples

 > $\mathrm{simplify}\left(\mathrm{Ei}\left(1,Ix\right)+\mathrm{Ei}\left(1,-Ix\right)\right)$
 ${I}{}\left({\mathrm{csgn}}{}\left({x}\right){-}{1}\right){}{\mathrm{\pi }}{}{\mathrm{csgn}}{}\left({I}{}{x}\right){-}{2}{}{\mathrm{Ci}}{}\left({x}\right)$ (1)
 > $\mathrm{simplify}\left(\mathrm{Ei}\left(1,Ix\right)-\mathrm{Ei}\left(1,-Ix\right)\right)$
 ${-I}{}\left({\mathrm{\pi }}{}{\mathrm{csgn}}{}\left({x}\right){-}{2}{}{\mathrm{Si}}{}\left({x}\right)\right)$ (2)