diff --git a/LICENSE.md b/LICENSE.md
index 182bf15..10cf005 100644
--- a/LICENSE.md
+++ b/LICENSE.md
@@ -20,3 +20,29 @@ The StatsFuns.jl package is licensed under the MIT "Expat" License:
 > CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 > TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 > SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+Portions are also under the (essentially equivalent) Boost Software License:
+
+> Boost Software License - Version 1.0 - August 17th, 2003
+>
+> Permission is hereby granted, free of charge, to any person or organization
+> obtaining a copy of the software and accompanying documentation covered by
+> this license (the "Software") to use, reproduce, display, distribute,
+> execute, and transmit the Software, and to prepare derivative works of the
+> Software, and to permit third-parties to whom the Software is furnished to
+> do so, all subject to the following:
+>
+> The copyright notices in the Software and this entire statement, including
+> the above license grant, this restriction and the following disclaimer,
+> must be included in all copies of the Software, in whole or in part, and
+> all derivative works of the Software, unless such copies or derivative
+> works are solely in the form of machine-executable object code generated by
+> a source language processor.
+>
+> THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+> IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+> FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+> SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+> FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+> ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+> DEALINGS IN THE SOFTWARE.
diff --git a/Project.toml b/Project.toml
index 58e58c8..ae01eb8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "StatsFuns"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "2.1.0"
+version = "2.2.0"
 
 [deps]
 HypergeometricFunctions = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
diff --git a/README.md b/README.md
index 5c22877..963965c 100644
--- a/README.md
+++ b/README.md
@@ -61,7 +61,9 @@ softmax!,       # inplace softmax
 
 # misc
 logmvgamma,     # logarithm of multivariate gamma function
-lstirling_asym
+lstirling_asym,
+
+owens_t         # Owen's T function
 ```
 
 ## Distribution-related functions
diff --git a/ext/StatsFunsChainRulesCoreExt.jl b/ext/StatsFunsChainRulesCoreExt.jl
index e94e549..78523cf 100644
--- a/ext/StatsFunsChainRulesCoreExt.jl
+++ b/ext/StatsFunsChainRulesCoreExt.jl
@@ -1,7 +1,8 @@
 module StatsFunsChainRulesCoreExt
 
 using StatsFuns
-using StatsFuns: digamma
+using SpecialFunctions: digamma, erf
+
 import ChainRulesCore
 
 ChainRulesCore.@scalar_rule(
@@ -82,4 +83,12 @@ ChainRulesCore.@scalar_rule(
     ),
 )
 
+ChainRulesCore.@scalar_rule(
+    owens_t(h::Real, a::Real),
+    (
+        normpdf(h) * erf((h * a) * invsqrt2) / -2,
+        inv2π * exp(-h^2 * (1 + a^2) / 2) / (1 + a^2),
+    ),
+)
+
 end # module
diff --git a/src/StatsFuns.jl b/src/StatsFuns.jl
index 3a39252..1ce7ed2 100644
--- a/src/StatsFuns.jl
+++ b/src/StatsFuns.jl
@@ -4,7 +4,7 @@ using Base: Math.@horner
 using Reexport: @reexport
 using Rmath: Rmath
 using SpecialFunctions: beta_inc, beta_inc_inv, digamma,
-    erfc, erfcinv, erfcx, gamma_inc, gamma_inc_inv, logbeta, loggamma
+    erf, erfc, erfcinv, erfcx, gamma_inc, gamma_inc_inv, logbeta, loggamma
 
 # reexports
 @reexport using IrrationalConstants:
@@ -260,11 +260,15 @@ export
     logmvbeta, # logarithm of multivariate beta function
     lstirling_asym,
 
+    # owens_t
+    owens_t,
+
     # tvpack
     bvncdf    # bivariate standard normal cdf
 
 ## source files
 include("misc.jl")
+include("owens_t.jl")
 include("tvpack.jl")
 
 include("distrs/beta.jl")
diff --git a/src/owens_t.jl b/src/owens_t.jl
new file mode 100644
index 0000000..53176d4
--- /dev/null
+++ b/src/owens_t.jl
@@ -0,0 +1,235 @@
+# Owen's T function
+#
+# Ported from Boost owen_t.hpp, which is Copyright Benjamin Sobotta 2012
+#      Use, modification and distribution are subject to the
+#      Boost Software License, Version 1.0. (http://www.boost.org/LICENSE_1_0.txt)
+# Port by Steven G. Johnson, also under Boost Software License, Version 1.0.
+#
+# Algorithm based on Mike Patefield and David Tandy, "Fast and accurate calculation
+# of Owen's T-function," Journal of Statistical Software, 5, pp. 1-25 (2000).
+
+# P(-∞<Z<=x)-0.5 with Z being normally distributed.
+owens_t_znorm1(x::Real) = erf(x * invsqrt2) / 2
+
+# Auxiliary function, it computes an array key that is used to determine
+# the specific computation method for Owen's T and the order thereof
+# used in owens_t_dispatch.  Differs from C++ in using 1-based indices
+const owens_t_hrange = (0.02f0, 0.06f0, 0.09f0, 0.125f0, 0.26f0, 0.4f0, 0.6f0, 1.6f0, 1.7f0, 2.33f0, 2.4f0, 3.36f0, 3.4f0, 4.8f0) # length 14
+const owens_t_arange = (0.025f0, 0.09f0, 0.15f0, 0.36f0, 0.5f0, 0.9f0, 0.99999f0) # length 7
+const owens_t_select = (
+    1, 1, 2, 13, 13, 13, 13, 13, 13, 13, 13, 16, 16, 16, 9,
+    1, 2, 2, 3, 3, 5, 5, 14, 14, 15, 15, 16, 16, 16, 9,
+    2, 2, 3, 3, 3, 5, 5, 15, 15, 15, 15, 16, 16, 16, 10,
+    2, 2, 3, 5, 5, 5, 5, 7, 7, 16, 16, 16, 16, 16, 10,
+    2, 3, 3, 5, 5, 6, 6, 8, 8, 17, 17, 17, 12, 12, 11,
+    2, 3, 5, 5, 5, 6, 6, 8, 8, 17, 17, 17, 12, 12, 12,
+    2, 3, 4, 4, 6, 6, 8, 8, 17, 17, 17, 17, 17, 12, 12,
+    2, 3, 4, 4, 6, 6, 18, 18, 18, 18, 17, 17, 17, 12, 12,
+) # 1-based indices (in 8x15 "matrix")
+function owens_t_compute_code(h::Float64, a::Float64)
+    ihint = something(findfirst(>=(h), owens_t_hrange), length(owens_t_hrange) + 1)
+    iaint = something(findfirst(>=(a), owens_t_arange), length(owens_t_arange) + 1)
+    return owens_t_select[(iaint - 1) * 15 + ihint]
+end
+
+const owens_t_ord = (2, 3, 4, 5, 7, 10, 12, 18, 10, 20, 30, 0, 4, 7, 8, 20, 0, 0) # 53-bit precision table
+function owens_t_get_order(icode::Int, ::Type{Float64})
+    return owens_t_ord[icode]
+end
+
+# compute the value of Owen's T function with method T1 from the reference paper
+function owens_t_T1(h::Float64, a::Float64, m::Int)
+    hs = -h * h / 2
+    as = a * a
+    aj = a * inv2π
+    dj = expm1(hs)
+    gj = hs * exp(hs)
+    val = atan(a) * inv2π
+    j, jj = one(m), oftype(h, 1)
+    while true
+        val += dj * aj / jj
+        m <= j && break
+        j += one(m)
+        jj += 2
+        aj *= as
+        dj = gj - dj
+        gj *= hs / j
+    end
+    return val
+end
+
+# compute the value of Owen's T function with method T2 from the reference paper
+function owens_t_T2(h::Float64, a::Float64, m::Int, ah::Float64)
+    maxii = m + m + one(m)
+    hs = h * h
+    as = -a * a
+    y = inv(hs)
+    ii = one(m)
+    val = zero(h)
+    vi = a * normpdf(ah)
+    z = owens_t_znorm1(ah) / h
+    while true
+        val += z
+        maxii <= ii && break
+        z = y * (vi - ii * z)
+        vi *= as
+        ii += oftype(ii, 2)
+    end
+    return val * normpdf(h)
+end
+
+# compute the value of Owen's T function with method T3 from the reference paper
+const owens_t_c2 = (
+    0.9999999999999998751, -0.99999999999988796462, 0.99999999998290743652,
+    -0.99999999896282500134, 0.99999996660459362918, -0.9999993398627247676,
+    0.99999125611136965852, -0.99991777624463387686, 0.99942835555870132569,
+    -0.99697311720723000295, 0.98751448037275303682, -0.95915857980572882813,
+    0.89246305511006708555, -0.76893425990463999675, 0.5889352846848469325,
+    -0.38380345160440256652, 0.20317601701045299653, -0.82813631607004984866e-1,
+    0.24167984735759576523e-1, -0.44676566663971825242e-2, 0.39141169402373836468e-3,
+)
+function owens_t_T3(h::Float64, a::Float64, ah::Float64)
+    as = a * a
+    hs = h * h
+    y = inv(hs)
+    ii = one(h)
+    vi = a * normpdf(ah)
+    zi = owens_t_znorm1(ah) / h
+    val = zero(h)
+    i = 1
+    while true
+        val += zi * owens_t_c2[i]
+        i == lastindex(owens_t_c2) && break
+        i += 1
+        zi = y * (ii * zi - vi)
+        vi *= as
+        ii += 2
+    end
+    return val * normpdf(h)
+end
+
+# compute the value of Owen's T function with method T4 from the reference paper
+function owens_t_T4(h::Float64, a::Float64, m::Int)
+    maxii = m + m + one(m)
+    hs = h * h
+    as = -a * a
+    ii = 1
+    ai = a * exp(-hs * (1 - as) / 2) * inv2π
+    yi = one(h)
+    val = zero(h)
+    while true
+        val += ai * yi
+        maxii <= ii && break
+        ii += 2
+        yi = (1 - hs * yi) / ii
+        ai *= as
+    end
+    return val
+end
+
+# compute the value of Owen's T function with method T5 from the reference paper
+const owens_t_pts = (
+    0.35082039676451715489e-2, 0.3127904233803075374e-1, 0.8526682628321945109e-1,
+    0.16245071730812277011, 0.25851196049125434828, 0.36807553840697533536,
+    0.48501092905604697475, 0.60277514152618576821, 0.71477884217753226516,
+    0.81475510988760098605, 0.89711029755948965867, 0.95723808085944261843, 0.99178832974629703586,
+)
+const owens_t_wts = (
+    0.18831438115323502887e-1, 0.18567086243977649478e-1, 0.18042093461223385584e-1,
+    0.17263829606398753364e-1, 0.1624321997598985673e-1, 0.14994592034116704829e-1,
+    0.13535474469662088392e-1, 0.11886351605820165233e-1, 0.10070377242777431897e-1,
+    0.81130545742299586629e-2, 0.60419009528470238773e-2, 0.38862217010742057883e-2, 0.16793031084546090448e-2,
+)
+#=
+    NOTICE:
+    - The pts[] array contains the squares (!) of the abscissas, i.e. the roots of the Legendre
+        polynomial P_n(x), instead of the plain roots as required in Gauss-Legendre
+        quadrature, because T5(h,a,m) contains only x^2 terms.
+    - The wts[] array contains the weights for Gauss-Legendre quadrature scaled with a factor
+        of 1/(2*pi) according to T5(h,a,m).
+=#
+function owens_t_T5(h::Float64, a::Float64)
+    as = a * a
+    hs = -h * h / 2
+    r = 1 .+ as .* owens_t_pts
+    return sum(owens_t_wts .* exp.(hs .* r) ./ r) * a
+end
+
+# compute the value of Owen's T function with method T6 from the reference paper
+function owens_t_T6(h::Float64, a::Float64)
+    normh = normccdf(h)
+    y = 1 - a
+    r = atan(y, 1 + a)
+    val = normh * (1 - normh) / 2
+    !iszero(r) && (val -= r * exp(-y * h * h / 2r) * inv2π)
+    return val
+end
+
+# This routine dispatches the call to one of six subroutines, depending on the values of h and a.
+# preconditions: h >= 0, 0<=a<=1, ah=a*h.
+# Simple main case for 64-bit precision or less, this is as per the Patefield-Tandy paper:
+function owens_t_dispatch(h::Float64, a::Float64, ah::Float64)
+    # Handle some special cases first, these are from
+    # page 1077 of Owen's original paper:
+    iszero(h) && return atan(a) * inv2π
+    iszero(a) && return zero(h)
+    a == 1 && return normccdf(-h) * normccdf(h) / 2
+    @assert a <= 1 # when a>1 we call this routine with 1/a:
+
+    icode = owens_t_compute_code(h, a)
+    m = owens_t_get_order(icode, typeof(h))
+    meth = (1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6) # 18 entries
+    method = meth[icode]
+
+    # determine the appropriate method, T1 ... T6
+    method == 1 && return owens_t_T1(h, a, m)
+    method == 2 && return owens_t_T2(h, a, m, ah)
+    method == 3 && return owens_t_T3(h, a, ah)
+    method == 4 && return owens_t_T4(h, a, m)
+    method == 5 && return owens_t_T5(h, a)
+    return owens_t_T6(h, a)
+end
+
+# compute Owen's T function, T(h,a), for arbitrary values of h and a
+function _owens_t(h::Float64, a::Float64)
+    # exploit that T(-h,a) == T(h,a)
+    h = abs(h)
+
+    # Use equation (2) in the paper to remap the arguments
+    # such that h>=0 and 0<=a<=1 for the call of the actual
+    # computation routine.
+    abs_a = abs(a)
+    abs_ah = abs_a * h
+
+    val = if abs_a <= 1
+        owens_t_dispatch(h, abs_a, abs_ah)
+    elseif !isfinite(abs_a)
+        isnan(abs_a) ? oftype(h, NaN) : normcdf(-h) / 2
+    elseif h <= oftype(h, 0.67)
+        normh = owens_t_znorm1(h)
+        normah = owens_t_znorm1(abs_ah)
+        1 // 4 - normh * normah - owens_t_dispatch(abs_ah, inv(abs_a), h)
+    else
+        normh = normccdf(h)
+        normah = normccdf(abs_ah)
+        (normh + normah) / 2 - normh * normah - owens_t_dispatch(abs_ah, inv(abs_a), h)
+    end
+    return copysign(val, a) # exploit that T(h,-a) == -T(h,a)
+end
+
+_owens_t(h::Float32, a::Float32) = Float32(owens_t(Float64(h), Float64(a)))
+_owens_t(h::Float16, a::Float16) = Float16(owens_t(Float64(h), Float64(a)))
+
+"""
+    owens_t(h::Real, a::Real)
+
+Return [Owen's T function](https://en.wikipedia.org/wiki/Owen%27s_T_function)
+
+```math
+T(h, a) = \\frac{1}{2\\pi} \\int_0^a \\frac{e^{-h^2(1+x^2)/2}}{1 + x^2} \\, dx
+```
+
+This is the probability of ``X > h`` and ``0 < Y < aX``, where ``X`` and ``Y`` are
+i.i.d. standard normal random variables.
+"""
+owens_t(h::Real, a::Real) = _owens_t(map(float, promote(h, a))...)
diff --git a/test/chainrules.jl b/test/chainrules.jl
index d59b5ea..2945f85 100644
--- a/test/chainrules.jl
+++ b/test/chainrules.jl
@@ -50,4 +50,9 @@ using Random
     _, pb = rrule(poislogpdf, 0.0, 1)
     _, x̄1, _ = pb(1)
     @test x̄1 == Inf
+
+    h = randn()
+    a = randn()
+    test_frule(owens_t, h, a)
+    test_rrule(owens_t, h, a)
 end
diff --git a/test/owens_t.jl b/test/owens_t.jl
new file mode 100644
index 0000000..740be87
--- /dev/null
+++ b/test/owens_t.jl
@@ -0,0 +1,456 @@
+using Test, StatsFuns
+
+# test data (h, a, exact) from https://github.com/boostorg/math/blob/13c0bc89632d745b991a1920c9bd697edaf6f60d/test/owens_t.ipp
+owens_t_test_data(T) = [
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02"), parse(T, "2.2942365980155351117754771526378292708740231264960539316842063696200884829628237039895484898529192823e-03")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "2.9680322689154555657058017082736661495213677947212098762543622722763825563827711568131850564334565506e-03")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "3.1597654248037660387449520543820166351754668510505531823382492970457382200077558044792256804713386129e-03")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "4.3232953135233836153944327583670440589476418747370390302105974330237550687887327299360596774532791101e-03")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "5.0100550889644229746912561152386170907268949874219104978095620802138249447202878889126283209658742296e-03")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "6.1497543339940146251856615610147485246423382395107105527248575888794201708943383385544040841893167983e-03")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "6.7002307780595028311848002054681870716943983498717211440016321757838493256869247382910637200137362515e-03")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.0087628098924846553420452991323128540455257919474718546084030038511341392097627616477463678020520866e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.0091132928374177373986149936548570045661635017241761865456752105413011145950758665503631981469962091e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.0865842961288026187893734175479235962324504288027096290482416005557459196544605743966959957549259912e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.1928879205559397161128411536383665386049060100190891105612351797899324440156577849032776806264950516e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2007404932089150629318599721043926151201252590201116565157838995615594563567446592356739043515060955e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2234231937902890618076422454559854736034641208834938001805660215261543653258044507100832640227607205e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2254641258057330150164973433843452155232009681583050905550399458557126941497853232806334014703269603e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2360475720884925881580539738830093572012024162485856485613974712653546627243019666702904836835836072e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2376176601227851086722830167717452814836846810367599158215995631280835335070487840750421239628452270e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2382005445939933843659988418503656684093356069262317993257524956338275590041101050569009428193352371e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2384419169235315605535269562348458006973333200556008698543822798769741450130359222839946856017776574e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2431007739121873243331263486394085638096884194270101674004097829060031548768693191305694357247777346e-02")),
+    (parse(T, "1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00"), parse(T, "9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "1.2437508801776841503931807680295142938639719448531279010032010195899482047937342387190771017427394090e-02")),
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+    (parse(T, "1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01"), parse(T, "9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "5.6765941572108102929182392406617202048399346202690008425365121190758925912633751741867242391943135847e-89")),
+    (parse(T, "1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01"), parse(T, "9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "5.6765941572108102929182392406617202048399346202690008425365121190758925914149018322974493002246798279e-89")),
+    (parse(T, "1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01"), parse(T, "9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "5.6765941572108102929182392406617202048399346202690008425365121190758925914149018421601995655864249226e-89")),
+    (parse(T, "1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01"), parse(T, "9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "5.6765941572108102929182392406617202048399346202690008425365121190758925914149018425679363648779892917e-89")),
+    (parse(T, "1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01"), parse(T, "9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "5.6765941572108102929182392406617202048399346202690008425365121190758925914149018426440620859348118110e-89")),
+    (parse(T, "1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01"), parse(T, "9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "5.6765941572108102929182392406617202048399346202690008425365121190758925914149018427767218487038675738e-89")),
+    (parse(T, "1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01"), parse(T, "9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01"), parse(T, "5.6765941572108102929182392406617202048399346202690008425365121190758925914149018427767301460804161903e-89")),
+]
+
+@testset "owens_t" begin
+    for (h, a, exact) in owens_t_test_data(Float64)
+        @test owens_t(h, a) ≈ exact rtol = 1.0e-15
+    end
+
+    # more test cases to exercise code not covered by Boost unit tests (grrr),
+    # with exact values provided by Mathematica OwenT function
+    for (h, a, exact) in [
+            (0.25, 1.0, 0.1201285306350882961916795008052213635794162711915703756065857717),
+            (0.125, 0.75, 0.1014881460301621857323787075087569394576179047696021721280270281),
+            (17 // 10, 0.75, 0.0194899019245137729112457194853956485135759661247399901776078745),
+            (12345 // 10^4, 99998 // 10^5, 0.0483667868485178158304070810789517218809603201932323103522462037),
+            (12345 // 10^4, 999991 // 10^6, 0.0483669775430142794579631531206838574627160460689072131897602482),
+            (66 // 100, 1.25, 0.1056698620377354634862871538372326581457639488972136894838517701),
+            (68 // 100, 1.25, 0.1037649136099534946378771146515761537424414280327623051479952043),
+            (0, Inf, 0.25),
+            (0, 1.0e300, 0.25),
+            (0.1, Inf, 0.2300860813614855092672976908804089584929688581551144836657589839),
+            (0.1, 1.0e300, 0.2300860813614855092672976908804089584929688581551144836657589839),
+            (37, 1 // 10, 2.862174895018181354817391600340565355765740911010979654675e-300),
+        ]
+        @test owens_t(h, a) ≈ exact rtol = 1.0e-15
+    end
+
+    # type stability
+    @inferred owens_t(0.1, 0.2)
+
+    # extremes:
+    @test owens_t(Inf, Inf) === 0.0
+    @test owens_t(1.0e300, 1.0e300) === 0.0
+    @test owens_t(Inf, -Inf) === -0.0
+    @test owens_t(-Inf, Inf) === 0.0
+    @test owens_t(-Inf, -Inf) === -0.0
+    @test owens_t(0, NaN) === NaN
+    @test owens_t(Inf, NaN) === NaN
+    for h in (NaN, Inf, 0.0, 0.1)
+        @test owens_t(h, 0.0) === 0.0
+        @test owens_t(h, -0.0) === -0.0
+    end
+    for a in (-0.1, 0.1)
+        @test owens_t(0, a) ≈ atan(a) / 2π rtol = 1.0e-15
+    end
+    @test owens_t(38, 0.1) ≈ 1.442507616809223311703254728848229952266052672515225305781e-316 rtol = 1.0e-7 # subnormal
+
+    # Float32 and Float16
+    @test owens_t(0.25f0, 0.5f0) == Float32(owens_t(0.25, 0.5))
+    @test owens_t(Float16(0.25), Float16(0.5)) == Float16(owens_t(0.25, 0.5))
+    @test owens_t(1, 2)::Float64 ≈ 0.0784681869930840963449419956315630528597353240494991328142744082 rtol = 1.0e-15
+    @test owens_t(1, 2.0f0)::Float32 ≈ 0.07846819f0 rtol = 1.0e-7
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 0cd38a1..dbf7258 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,4 +1,4 @@
-tests = ["rmath", "generic", "misc", "chainrules", "inverse", "tvpack", "qa"]
+tests = ["owens_t", "rmath", "generic", "misc", "chainrules", "inverse", "tvpack", "qa"]
 
 for t in tests
     fp = "$t.jl"