This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

ExpIntegralE

ExpIntegralE
gives the exponential integral function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
  • ExpIntegralE has a branch cut discontinuity in the complex z plane running from - to 0.
  • For certain special arguments, ExpIntegralE automatically evaluates to exact values.
  • ExpIntegralE can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Series for generic and logarithmic cases:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
In[1]:=
Click for copyable input
Out[1]=
 
Series for generic and logarithmic cases:
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:
Complex arguments:
Infinite arguments give exact results:
ExpIntegralE threads element-wise over lists and arrays:
ExpIntegralE can be applied to power series:
Series expansion at infinity:
Give the result for an arbitrary symbolic direction:
Plot over the complex plane:
Solution of the heat equation for piecewise-constant initial conditions:
Check that the solution satisfies the heat equation:
Plot the solution for different times:
Calculate a classic asymptotic series:
Plot the difference of a truncated series and the exponential integral sum:
Use FullSimplify to simplify exponential integrals:
Use FunctionExpand to express special cases in simpler functions:
Numerically find a root of a transcendental equation:
Generate from integrals, sums, and differential equations:
ExpIntegralE appears as special cases of hypergeometric functions:
Integrals:
ExpIntegralE is a numeric function:
Large arguments can give results too large to be computed explicitly:
Machine-number inputs can give high-precision results:
In TraditionalForm, E_n(z) is not automatically interpreted as an exponential integral:
Plot the Riemann surface of :
New in 1