gives the Whittaker function .
- 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 .
- WhittakerW can be used with Interval and CenteredInterval objects. »
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 (5)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
WhittakerW can be used with Interval and CenteredInterval objects:
Specific Values (7)
WhittakerW for symbolic parameters:
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 as real parts of two parameters vary:
Types 2 and 3 of WhittakerW function have different branch cut structures:
Function Properties (11)
Complex domain of WhittakerW:
WhittakerW may reduce to simpler functions:
WhittakerW threads elementwise over lists:
WhittakerW is not an analytic function:
is neither non-decreasing nor non-increasing on its real domain:
is neither non-negative nor non-positive on its real domain:
WhittakerW has both singularity and discontinuity in (-∞,0]:
is neither convex nor concave on its real domain:
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 :
Properties & Relations (4)
Use FunctionExpand to expand WhittakerW into other functions:
Integrate expressions involving Whittaker functions:
WhittakerW can be represented as a DifferentialRoot:
WhittakerW can be represented as a DifferenceRoot:
Wolfram Research (2007), WhittakerW, Wolfram Language function, https://reference.wolfram.com/language/ref/WhittakerW.html.
Wolfram Language. 2007. "WhittakerW." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WhittakerW.html.
Wolfram Language. (2007). WhittakerW. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WhittakerW.html