Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number input:

Evaluate efficiently at high precision:

WhittakerM can be used with Interval and CenteredInterval objects:

Compute the elementwise values of an array:

Or compute the matrix WhittakerM function using MatrixFunction:

WhittakerM for symbolic parameters:

Values at zero:

Find the first positive maximum of WhittakerM[5,1/2,x]:

Compute the associated WhittakerM[3,1/2,x] function:

Compute the associated WhittakerM function for half-integer parameters:

Different cases of WhittakerM give different symbolic forms:

WhittakerM threads elementwise over lists:

Plot the WhittakerM function for various orders:

Plot the real part of :

Plot the imaginary part of :

Plot as real parts of two parameters vary:

Real domain of :

Complex domain of WhittakerM:

Approximate range of :

WhittakerM may reduce to simpler functions:

is not an analytic function of for integer values of :

Nor is it meromorphic:

It is analytic for other values of :

is neither non-decreasing nor non-increasing:

is not injective:

is not surjective:

is neither non-negative nor non-positive on its real domain:

WhittakerM has both singularity and discontinuity in (-∞,0]:

is neither convex nor concave on its real domain:

TraditionalForm formatting:

First derivative with respect to z:

Higher derivatives with respect to z when k=1/3 and m=1/2:

Plot the higher derivatives with respect to z when k=1/3 and m=1/2:

Formula for the derivative with respect to z:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

General term in the series expansion using SeriesCoefficient:

Find the series expansion at Infinity:

Find series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point: