Mathematica 9 is now available
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > Bessel-Related Functions >
Built-in Mathematica SymbolTutorials »|See Also »|More About »

HankelH2

HankelH2[n, z]
gives the Hankel function of the second kind .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • is given by J_n(z)-iY_n(z).
  • HankelH1[n, z] has a branch cut discontinuity in the complex z plane running from -infty to 0.
  • For certain special arguments, HankelH2 automatically evaluates to exact values.
  • HankelH2 can be evaluated to arbitrary numerical precision.
  • HankelH2 automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (3)
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]=
Scope   (6)
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:
Generalizations & Extensions   (1)
HankelH2 can be applied to a power series:
Properties & Relations   (2)
Use FunctionExpand to convert to Bessel functions:
Integrate expressions with HankelH2:
Possible Issues   (1)
HankelH2 does not automatically evaluate symbolically for half-integer arguments:
Use FunctionExpand to obtain expanded form:
New in 6
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team