SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Built-in Mathematica Symbol

WhittakerM

WhittakerM[k, m, z]
gives the Whittaker function

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

WhittakerM[k, m, z] 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:

Plot

Use FunctionExpand to expand in terms of hypergeometric functions:

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: