OwenT
OwenT[x,a]
gives Owen's T function .
Details

- Mathematical function, suitable for both symbolic and numerical evaluation.
for real
.
- OwenT[x,a] is an 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.
Examples
open allclose allBasic 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:
Scope (30)
Numerical Evaluation (4)
Specific Values (5)
Visualization (3)
Plot the OwenT function for various parameters:
Function Properties (11)
OwenT is defined for all real values:
is even with respect to
and odd with respect to
:
OwenT may reduce to a simpler form:
OwenT is an analytic function:
OwenT is neither non-decreasing nor non-increasing:
OwenT has no singularities or discontinuities:
OwenT is neither convex nor concave:
TraditionalForm formatting:
Differentiation (2)
Integration (3)
Compute the indefinite integral using Integrate:
Series Expansions (2)
Find the Taylor expansion using Series:
Applications (5)
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:
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 :
Text
Wolfram Research (2010), OwenT, Wolfram Language function, https://reference.wolfram.com/language/ref/OwenT.html.
CMS
Wolfram Language. 2010. "OwenT." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/OwenT.html.
APA
Wolfram Language. (2010). OwenT. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/OwenT.html