- Mathematical function, suitable for both symbolic and numerical manipulation.
- WhittakerW is related to the confluent hypergeometric function by .
- is infinite at for integer .
- For certain special arguments, WhittakerW automatically evaluates to exact values.
- WhittakerW can be evaluated to arbitrary numerical precision.
- WhittakerW automatically threads over lists.
- WhittakerW[k,m,z] has a branch cut discontinuity in the complex plane running from to .
Examplesopen allclose all
Basic Examples (6)
Use FunctionExpand to expand in terms of hypergeometric functions:
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Numerical Evaluation (4)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number input:
Evaluate efficiently at high precision:
Specific Values (7)
WhittakerW for symbolic parameters:
Values at zero:
Evaluate symbolically at the origin:
Find the first positive maximum of WhittakerW[3,1/2,x]:
Compute the associated WhittakerW[3,1/2,x] function:
Compute the associated WhittakerW function for half-integer parameters:
Different WhittakerW types give different symbolic forms:
Plot the WhittakerW function for various orders:
Plot the real part of :
Plot the imaginary part of :
Plot as real parts of two parameters vary:
Types 2 and 3 of WhittakerW function have different branch cut structures:
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:
Series Expansions (5)
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:
Green's function of the 3D Coulomb potential:
Properties & Relations (4)