gives Owen's T function .
- Mathematical function, suitable for both symbolic and numerical evaluation.
- for real .
- OwenT[x,a] is the entire function of x with no branch cut discontinuities.
- OwenT[x,a] has a branch cut discontinuity in the complex a plane running from to and from to .
- For certain special arguments, OwenT automatically evaluates to exact values.
- OwenT can be evaluated to arbitrary numerical precision.
- OwenT automatically threads over lists.
Examplesopen allclose all
Basic Examples (6)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Series expansion at a singular point:
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 (5)
Values of OwenT at fixed points:
OwenT for symbolic a:
Values at zero:
Find the first positive maximum of OwenT[x,1 ]:
Compute the associated OwenT[x,1] function:
Plot the OwenT function for various parameters:
Plot the real part of :
Plot the imaginary part of :
Plot as real parts of two parameters vary:
Types 2 and 3 of OwenT function have different branch cut structures:
Function Properties (4)
OwenT is defined for all real and complex values:
Owen's T function is even with respect to x and odd with respect to a:
OwenT may reduce to a simpler form:
First derivative with respect to x:
First derivative with respect to a:
Higher derivatives with respect to x:
Plot the higher derivatives with respect to x when a=1.5:
Compute the indefinite integral using Integrate:
Verify the anti-derivative:
Series Expansions (2)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
Taylor expansion at a generic point:
Plot Owen's T-function in the complex a plane:
Compute the CDF of SkewNormalDistribution:
Compute the probability of an uncorrelated bivariate normal over a truncated wedge:
The probability for a standard binormal variate with correlation to lie inside a triangle can be expressed using OwenT:
Visualize the region:
Evaluate the probability for a particular value of the correlation coefficient:
Use NProbability to compute the probability directly:
Use OwenT to compute the standard BinormalDistribution probability of :
Properties & Relations (1)