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WhittakerW

WhittakerW[k, m, z]
gives the Whittaker function W_(k,m)(z).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • WhittakerW is related to the confluent hypergeometric function by .
  • W_(k,m)(z) is infinite at z=0 for integer m>0.
  • For certain special arguments, WhittakerW automatically evaluates to exact values.
  • WhittakerW can be evaluated to arbitrary numerical precision.
  • WhittakerW[k, m, z] has a branch cut discontinuity in the complex z plane running from -infty to 0.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Evaluate numerically:
Plot W_(2,1/2)(x):
Use FunctionExpand to expand in terms of hypergeometric functions:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
Plot W_(2,1/2)(x):
In[1]:=
Click for copyable input
Out[1]=
 
Use FunctionExpand to expand in terms of hypergeometric functions:
In[1]:=
Click for copyable input
Out[1]=
Scope   (7)
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Evaluate symbolically at the origin:
WhittakerW threads element-wise over lists:
Series expansion:
TraditionalForm formatting:
Applications   (1)
Green's function of the 3D Coulomb potential:
Properties & Relations   (2)
Use FunctionExpand to expand WhittakerW into other functions:
Integrate expressions involving Whittaker functions:
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