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BUILT-IN MATHEMATICA SYMBOL

WhittakerM

gives the Whittaker function

For certain special arguments, WhittakerM automatically evaluates to exact values.

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:

Out[1]=

Plot

Out[1]=

Use FunctionExpand to expand in terms of hypergeometric functions:

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:

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: