test_error_functions.py 文件源码

def test_ci():
    m1 = exp_polar(I*pi)
    m1_ = exp_polar(-I*pi)
    pI = exp_polar(I*pi/2)
    mI = exp_polar(-I*pi/2)

    assert Ci(m1*x) == Ci(x) + I*pi
    assert Ci(m1_*x) == Ci(x) - I*pi
    assert Ci(pI*x) == Chi(x) + I*pi/2
    assert Ci(mI*x) == Chi(x) - I*pi/2
    assert Chi(m1*x) == Chi(x) + I*pi
    assert Chi(m1_*x) == Chi(x) - I*pi
    assert Chi(pI*x) == Ci(x) + I*pi/2
    assert Chi(mI*x) == Ci(x) - I*pi/2
    assert Ci(exp_polar(2*I*pi)*x) == Ci(x) + 2*I*pi
    assert Chi(exp_polar(-2*I*pi)*x) == Chi(x) - 2*I*pi
    assert Chi(exp_polar(2*I*pi)*x) == Chi(x) + 2*I*pi
    assert Ci(exp_polar(-2*I*pi)*x) == Ci(x) - 2*I*pi

    assert Ci(oo) == 0
    assert Ci(-oo) == I*pi
    assert Chi(oo) == oo
    assert Chi(-oo) == oo

    assert mytd(Ci(x), cos(x)/x, x)
    assert mytd(Chi(x), cosh(x)/x, x)

    assert mytn(Ci(x), Ci(x).rewrite(Ei),
                Ei(x*exp_polar(-I*pi/2))/2 + Ei(x*exp_polar(I*pi/2))/2, x)
    assert mytn(Chi(x), Chi(x).rewrite(Ei),
                Ei(x)/2 + Ei(x*exp_polar(I*pi))/2 - I*pi/2, x)

    assert tn_arg(Ci)
    assert tn_arg(Chi)

    from sympy import O, EulerGamma, log, limit
    assert Ci(x).nseries(x, n=4) == \
        EulerGamma + log(x) - x**2/4 + x**4/96 + O(x**5)
    assert Chi(x).nseries(x, n=4) == \
        EulerGamma + log(x) + x**2/4 + x**4/96 + O(x**5)
    assert limit(log(x) - Ci(2*x), x, 0) == -log(2) - EulerGamma