Owen's T function

[1] The function T(h, a) gives the probability of the event (X > h and 0 < Y < aX) where X and Y are independent standard normal random variables.

This function can be used to calculate bivariate normal distribution probabilities[2][3] and, from there, in the calculation of multivariate normal distribution probabilities.

[4] It also frequently appears in various integrals involving Gaussian functions.

Computer algorithms for the accurate calculation of this function are available;[5] quadrature having been employed since the 1970s.

[6] Here Φ(x) is the standard normal cumulative distribution function More properties can be found in the literature.