def test_erf2():
assert erf2(0, 0) == S.Zero
assert erf2(x, x) == S.Zero
assert erf2(nan, 0) == nan
assert erf2(-oo, y) == erf(y) + 1
assert erf2(oo, y) == erf(y) - 1
assert erf2(x, oo) == 1 - erf(x)
assert erf2(x, -oo) == -1 - erf(x)
assert erf2(x, erf2inv(x, y)) == y
assert erf2(-x, -y) == -erf2(x, y)
assert erf2(-x, y) == erf(y) + erf(x)
assert erf2(x, -y) == -erf(y) - erf(x)
assert erf2(x, y).rewrite(
'fresnels') == erf(y).rewrite(fresnels) - erf(x).rewrite(fresnels)
assert erf2(x, y).rewrite(
'fresnelc') == erf(y).rewrite(fresnelc) - erf(x).rewrite(fresnelc)
assert erf2(
x, y).rewrite('hyper') == erf(y).rewrite(hyper) - erf(x).rewrite(hyper)
assert erf2(x, y).rewrite(
'meijerg') == erf(y).rewrite(meijerg) - erf(x).rewrite(meijerg)
assert erf2(
x,
y).rewrite('uppergamma'
) == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma)
assert erf2(
x,
y).rewrite('expint') == erf(y).rewrite(expint) - erf(x).rewrite(expint)
assert erf2(I, 0).is_real is False
assert erf2(0, 0).is_real is True
assert expand_func(erf(x) + erf2(x, y)) == erf(y)
assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y))
assert erf2(x, y).rewrite('erf') == erf(y) - erf(x)
assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y)
assert erf2(x, y).rewrite('erfi') == I * (erfi(I * x) - erfi(I * y))
assert erf2(x, y).diff(x) == erf2(x, y).fdiff(1)
assert erf2(x, y).diff(y) == erf2(x, y).fdiff(2)
assert erf2(x, y).diff(x) == -2 * exp(-x**2) / sqrt(pi)
assert erf2(x, y).diff(y) == 2 * exp(-y**2) / sqrt(pi)
raises(ArgumentIndexError, lambda: erf2(x, y).fdiff(3))
assert erf2(x, y).is_extended_real is None
xr, yr = symbols('xr yr', extended_real=True)
assert erf2(xr, yr).is_extended_real is True
def test_erf2():
assert erf2(0, 0) == S.Zero
assert erf2(x, x) == S.Zero
assert erf2(nan, 0) == nan
assert erf2(-oo, y) == erf(y) + 1
assert erf2( oo, y) == erf(y) - 1
assert erf2( x, oo) == 1 - erf(x)
assert erf2( x,-oo) == -1 - erf(x)
assert erf2(x, erf2inv(x, y)) == y
assert erf2(-x, -y) == -erf2(x,y)
assert erf2(-x, y) == erf(y) + erf(x)
assert erf2( x, -y) == -erf(y) - erf(x)
assert erf2(x, y).rewrite('fresnels') == erf(y).rewrite(fresnels)-erf(x).rewrite(fresnels)
assert erf2(x, y).rewrite('fresnelc') == erf(y).rewrite(fresnelc)-erf(x).rewrite(fresnelc)
assert erf2(x, y).rewrite('hyper') == erf(y).rewrite(hyper)-erf(x).rewrite(hyper)
assert erf2(x, y).rewrite('meijerg') == erf(y).rewrite(meijerg)-erf(x).rewrite(meijerg)
assert erf2(x, y).rewrite('uppergamma') == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma)
assert erf2(x, y).rewrite('expint') == erf(y).rewrite(expint)-erf(x).rewrite(expint)
assert erf2(I, 0).is_real is False
assert erf2(0, 0).is_real is True
assert expand_func(erf(x) + erf2(x, y)) == erf(y)
assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y))
assert erf2(x, y).rewrite('erf') == erf(y) - erf(x)
assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y)
assert erf2(x, y).rewrite('erfi') == I*(erfi(I*x) - erfi(I*y))
raises(ArgumentIndexError, lambda: erfi(x).fdiff(3))
def test_erf2():
assert erf2(0, 0) is S.Zero
assert erf2(x, x) is S.Zero
assert erf2(nan, 0) is nan
assert erf2(-oo, y) == erf(y) + 1
assert erf2(oo, y) == erf(y) - 1
assert erf2(x, oo) == 1 - erf(x)
assert erf2(x, -oo) == -1 - erf(x)
assert erf2(x, erf2inv(x, y)) == y
assert erf2(-x, -y) == -erf2(x, y)
assert erf2(-x, y) == erf(y) + erf(x)
assert erf2(x, -y) == -erf(y) - erf(x)
assert erf2(x, y).rewrite(
"fresnels") == erf(y).rewrite(fresnels) - erf(x).rewrite(fresnels)
assert erf2(x, y).rewrite(
"fresnelc") == erf(y).rewrite(fresnelc) - erf(x).rewrite(fresnelc)
assert erf2(
x, y).rewrite("hyper") == erf(y).rewrite(hyper) - erf(x).rewrite(hyper)
assert erf2(x, y).rewrite(
"meijerg") == erf(y).rewrite(meijerg) - erf(x).rewrite(meijerg)
assert erf2(
x,
y).rewrite("uppergamma"
) == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma)
assert erf2(
x,
y).rewrite("expint") == erf(y).rewrite(expint) - erf(x).rewrite(expint)
assert erf2(I, 0).is_real is False
assert erf2(0, 0).is_real is True
assert expand_func(erf(x) + erf2(x, y)) == erf(y)
assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y))
assert erf2(x, y).rewrite("erf") == erf(y) - erf(x)
assert erf2(x, y).rewrite("erfc") == erfc(x) - erfc(y)
assert erf2(x, y).rewrite("erfi") == I * (erfi(I * x) - erfi(I * y))
assert erf2(x, y).diff(x) == erf2(x, y).fdiff(1)
assert erf2(x, y).diff(y) == erf2(x, y).fdiff(2)
assert erf2(x, y).diff(x) == -2 * exp(-(x**2)) / sqrt(pi)
assert erf2(x, y).diff(y) == 2 * exp(-(y**2)) / sqrt(pi)
raises(ArgumentIndexError, lambda: erf2(x, y).fdiff(3))
assert erf2(x, y).is_extended_real is None
xr, yr = symbols("xr yr", extended_real=True)
assert erf2(xr, yr).is_extended_real is True
