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AngerJ

AngerJ[Nu, z]
gives the Anger function J_v(z).
AngerJ[Nu, Mu, z]
gives the associated Anger function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • J_nu(z) satisfies the differential equation z^2y^('')+zy^'+(z^2-nu^2)y=(z-nu)sin(pi nu)/pi.
  • J_nu(z) is defined by .
  • AngerJ[Nu, z] is an entire function of z with no branch cut discontinuities.
  • For certain special arguments, AngerJ automatically evaluates to exact values.
  • AngerJ can be evaluated to arbitrary numerical precision.
  • AngerJ automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Evaluate numerically:
Plot TemplateBox[{{1, /, 2}, x}, AngerJ2]:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
Plot TemplateBox[{{1, /, 2}, x}, AngerJ2]:
In[1]:=
Click for copyable input
Out[1]=
Scope   (6)
Evaluate for complex arguments:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
AngerJ threads element-wise over lists:
Simple exact values are generated automatically:
TraditionalForm formatting:
Properties & Relations   (1)
Use FunctionExpand to expand AngerJ into hypergeometric functions:
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