This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

ExpIntegralEi

ExpIntegralEi[z]
gives the exponential integral function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • , where the principal value of the integral is taken.
  • ExpIntegralEi[z] has a branch cut discontinuity in the complex z plane running from to .
  • For certain special arguments, ExpIntegralEi automatically evaluates to exact values.
Evaluate numerically:
Series expansion around the branch point at the origin:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
In[1]:=
Click for copyable input
Out[1]=
 
Series expansion around the branch point at the origin:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
Evaluate to high precision:
The precision of the output tracks the precision of the input:
ExpIntegralEi threads element-wise over lists:
ExpIntegralEi can take complex number inputs:
Simple exact values are generated automatically:
TraditionalForm formatting:
ExpIntegralEi can be applied to power series:
Find series expansions at infinity:
Give the result for an arbitrary symbolic direction:
Compute a classical asymptotic series with k! coefficients:
Plot the imaginary part in the complex plane:
Use FullSimplify to simplify expressions containing exponential integrals:
Find the numerical root:
Obtain ExpIntegralEi from integrals and sums:
Calculate limits:
Obtain ExpIntegralEi from a differential equation:
Calculate Wronskian:
Integrals:
Integral transforms:
ExpIntegralEi can take large values for moderate-size arguments:
ExpIntegralEi has a special value on the negative real axis, not obtained as a limit from either side:
A larger setting for $MaxExtraPrecision can be needed:
Nested integrals:
New in 1