This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

 LogIntegral[z]is the logarithmic integral function .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• The logarithmic integral function is defined by , where the principal value of the integral is taken.
• LogIntegral[z] has a branch cut discontinuity in the complex z plane running from to .
• For certain special arguments, LogIntegral automatically evaluates to exact values.
• LogIntegral can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Series expansion around the branch point at :
Evaluate numerically:
 Out[1]=

 Out[1]=

Series expansion around the branch point at :
 Out[1]=
 Scope   (7)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
LogIntegral can take complex number inputs:
Simple exact values are generated automatically:
Series expansions on either side of the branch point at :
LogIntegral can be applied to power series:
 Applications   (4)
Approximate number of primes less than :
Compare with exact counts:
Plot the real part in the complex plane:
Plot the absolute value in the complex plane:
Find an approximation to Soldner's constant :
Use FullSimplify to simplify expressions into logarithmic integrals:
Use FunctionExpand to write expressions in logarithmic integrals when possible:
Find the numerical root:
Obtain LogIntegral from integrals and sums:
Integrals:
In traditional form, parentheses are needed around the argument:
Nested integrals:
Plot the Riemann surface of LogIntegral:
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