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SinIntegral

SinIntegral[z]
gives the sine integral function ).
MORE INFORMATION
  • 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.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Evaluate numerically:
Plot :
Differentiate :
Series expansion at the origin:
Evaluate numerically:
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Click for copyable input
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Plot :
In[1]:=
Click for copyable input
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Differentiate :
In[1]:=
Click for copyable input
Out[1]=
 
Series expansion at the origin:
In[1]:=
Click for copyable input
Out[1]=
Scope   (5)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
SinIntegral threads element-wise over lists:
Simple exact values are generated automatically:
TraditionalForm formatting:
Generalizations & Extensions   (2)
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:
Properties & Relations   (7)
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:
Possible Issues   (2)
SinIntegral can take large values for moderate-size arguments:
A larger setting for $MaxExtraPrecision can be needed:
Neat Examples   (1)
Nested integrals:
New in 2
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