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

HankelH1

HankelH1
gives the Hankel function of the first kind .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • is given by .
  • HankelH1 has a branch cut discontinuity in the complex z plane running from to .
  • For certain special arguments, HankelH1 automatically evaluates to exact values.
  • HankelH1 can be evaluated to arbitrary numerical precision.
  • HankelH1 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:
HankelH1 threads element-wise over lists:
TraditionalForm formatting:
HankelH1 can be applied to a power series:
Find series expansions at infinity:
Use FunctionExpand to convert to Bessel functions:
Integrate expressions with HankelH1:
HankelH1 does not automatically evaluate symbolically for half-integer arguments:
Use FunctionExpand to obtain an expanded form:
New in 6