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HankelH2

HankelH2
gives the Hankel function of the second kind .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • is given by .
  • HankelH2 has a branch cut discontinuity in the complex z plane running from to .
  • For certain special arguments, HankelH2 automatically evaluates to exact values.
  • HankelH2 can be evaluated to arbitrary numerical precision.
  • HankelH2 automatically threads over lists.
Evaluate numerically:
Plot the absolute value of for various orders:
Series at the origin:
Series at infinity:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
Plot the absolute value of for various orders:
In[1]:=
Click for copyable input
Out[1]=
 
Series at the origin:
In[1]:=
Click for copyable input
Out[1]=
Series at infinity:
In[2]:=
Click for copyable input
Out[2]=
Evaluate for complex arguments and orders:
Evaluate numerically to high precision:
The precision of the output tracks the precision of the input:
HankelH2 threads element-wise over lists:
Use FunctionExpand to expand half-integer order HankelH2 into elementary functions:
TraditionalForm formatting:
HankelH2 can be applied to a power series:
Use FunctionExpand to convert to Bessel functions:
Integrate expressions with HankelH2:
HankelH2 does not automatically evaluate symbolically for half-integer arguments:
Use FunctionExpand to obtain expanded form:
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