Adds Owen's T function

[ValentinKaisermayer]

    using Plots, SpecialFunctions
    plot(-3:0.1:3, -3:0.1:3, owens_t, st=:surface)

julia> all(owens_t.(-3:3, 0) .== 0.)
true

julia> all(isapprox.(owens_t.(0, -3:3), 1 ./ (2 .* pi) .* atan.(-3:3), rtol=1e-6))
true

julia> all(isapprox.([owens_t(-h, a) for h in -3:3, a in -3:3], [owens_t(h, a) for h in -3:3, a in -3:3], rtol=1e-6))
true

julia> all(isapprox.([owens_t(h, -a) for h in -3:3, a in -3:3], [-owens_t(h, a) for h in -3:3, a in -3:3], rtol=1e-6))
true

[ValentinKaisermayer]

Ported from http://people.sc.fsu.edu/~jburkardt/m_src/asa005/tfn.m

[giordano]

Note that that file has the following license:

This code is distributed under the GNU LGPL license.

while this package has MIT License. As far as I know, LGPL is compatible with MIT license, but you must attribute the work to the original author and use the same license for this specific function, and I believe it'd be better to make it explicit in the license of this package that this function has a different license.

[stevengj]

This is more restrictive than the SpecialFunctions.jl license, which also disqualifies anything derived from that code.

[stevengj]

As far as I know, LGPL is compatible with MIT license

It's "compatible" in that you can legally comply with both licenses simultaneously, but it would effectively put SpecialFunctions.jl under the LGPL (since the terms of the LGPL are more restrictive than MIT, and with any license the copyright extends to all derived works including translations to other languages).

[ValentinKaisermayer]

Scipy implements a version from Boost.
Which in turn is based on the paper Patefield et al. - 2000 - Fast and Accurate Calculation of Owen's T Function.

[azev77]

@ohmsweetohm1 this would be really nice, as it would allow a CDF for SkewNormal in Distributions.jl

[ValentinKaisermayer]

Closing this, due to licencing issues