gives Owen's T function .
- 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 branch cut discontinuities in the complex a plane running 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)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (5)
Plot the OwenT function for various parameters:
Function Properties (11)
OwenT is defined for all real values:
OwenT may reduce to a simpler form:
OwenT is an analytic function in both its arguments:
OwenT is neither non-decreasing nor non-increasing:
OwenT has no singularities or discontinuities:
OwenT is neither convex nor concave:
Compute the indefinite integral with respect to using Integrate:
Series Expansions (2)
Find the Taylor expansion using Series:
Compute the CDF of SkewNormalDistribution:
The probability that a standard binormal variate with correlation lies within an equilateral triangle can be expressed using OwenT:
Use NProbability to compute the probability directly:
Wolfram Research (2010), OwenT, Wolfram Language function, https://reference.wolfram.com/language/ref/OwenT.html.
Wolfram Language. 2010. "OwenT." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/OwenT.html.
Wolfram Language. (2010). OwenT. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/OwenT.html