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WhittakerM

WhittakerM
gives the Whittaker function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • WhittakerM is related to the hypergeometric function by .
  • vanishes at for .
  • For certain special arguments, WhittakerM automatically evaluates to exact values.
  • WhittakerM can be evaluated to arbitrary numerical precision.
  • WhittakerM has a branch cut discontinuity in the complex plane running from to .
Evaluate numerically:
Plot :
Use FunctionExpand to expand in terms of hypergeometric functions:
Evaluate numerically:
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Click for copyable input
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Plot :
In[1]:=
Click for copyable input
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Use FunctionExpand to expand in terms of hypergeometric functions:
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Click for copyable input
Out[1]=
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:
WhittakerM threads element-wise over lists:
Series expansion:
TraditionalForm formatting:
The bound-state Coulomb eigenfunction in parabolic coordinates:
Decompose the eigenfunction in terms of spherical eigenfunctions:
Parabolic coordinates relate to radial coordinates as and :
Use FunctionExpand to expand WhittakerM into other functions:
Integrate expressions involving Whittaker functions:
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