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GeezerVison is showing mathworld.wolfram.com — Owen T-Function -- from Wolfram MathWorld

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Owen T-Function

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OwenTFunction

The Owen T-function is defined as

T(x,a)=1/(2pi)int_0^a(e^(-x^2(1+t^2)/2))/(1+t^2)dt
(1)

for a in R. It is implemented in the Wolfram Language as OwenT[x, a].

The function is symmetric about x=0 and antisymmetric about a=0, so

T(-x,a)=T(x,a)
(2)
T(x,-a)=-T(x,a).
(3)

Special values are given by

T(x,0)=0
(4)
T(x,1)=1/8erfc(-x/(sqrt(2)))erfc(x/(sqrt(2))),
(5)

where erfc is the complementary error function.

See also

Erf, Gaussian Function, Normal Distribution, Normal Distribution Function

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Cite this as:

Weisstein, Eric W. "Owen T-Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OwenT-Function.html

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