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

# SinIntegral

 SinIntegral[z]gives the sine integral function ).
• Mathematical function, suitable for both symbolic and numerical manipulation.
• .
• SinIntegral[z] is an entire function of with no branch cut discontinuities.
• For certain special arguments, SinIntegral automatically evaluates to exact values.
• SinIntegral can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Plot :
Differentiate :
Series expansion at the origin:
Evaluate numerically:
 Out[1]=

Plot :
 Out[1]=

Differentiate :
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Series expansion at the origin:
 Out[1]=
 Scope   (5)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
SinIntegral can be applied to power series:
Find series expansions at infinity:
Give the result for an arbitrary symbolic direction :
 Applications   (3)
Plot the absolute value in the complex plane:
Real part of the Euler-Heisenberg effective action:
Find a leading term in :
Gibbs phenomenon for a square wave:
Magnify the overshoot region:
Compute the asymptotic overshoot:
Parity transformation is automatically applied:
Use FullSimplify to simplify expressions containing sine integrals:
Find a numerical root:
Obtain SinIntegral from integrals and sums:
Obtain SinIntegral from a differential equation:
Calculate the Wronskian:
Compare with Wronskian:
Integrals:
Laplace transform:
SinIntegral can take large values for moderate-size arguments:
A larger setting for \$MaxExtraPrecision can be needed:
Nested integrals:
New in 2