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# sympy.mpmath.fp.e1

All Samples(510)  |  Call(510)  |  Derive(0)  |  Import(0)
Computes the exponential integral \mathrm{E}_1(z), given by

.. math ::

\mathrm{E}_1(z) = \int_z^{\infty} \frac{e^{-t}}{t} dt.

This is equivalent to :func:~mpmath.expint with n = 1.

**Examples**
(more...)


def test_fp_stress_ei_e1():
# Can be tightened on recent Pythons with more accurate math/cmath
ATOL = 1e-13
PTOL = 1e-12
v = fp.e1(1.1641532182693481445e-10)
assert ae(v, 22.296641293693077672, tol=ATOL)
assert type(v) is float
v = fp.e1(0.25)

    assert ae(v, 1.0442826344437381945, tol=ATOL)
assert type(v) is float
v = fp.e1(1.0)
assert ae(v, 0.21938393439552027368, tol=ATOL)
assert type(v) is float
v = fp.e1(2.0)
assert ae(v, 0.048900510708061119567, tol=ATOL)
assert type(v) is float
v = fp.e1(5.0)


def test_fp_stress_ei_e1():
# Can be tightened on recent Pythons with more accurate math/cmath
ATOL = 1e-13
PTOL = 1e-12
v = fp.e1(1.1641532182693481445e-10)
assert ae(v, 22.296641293693077672, tol=ATOL)
assert type(v) is float
v = fp.e1(0.25)

    assert ae(v, 1.0442826344437381945, tol=ATOL)
assert type(v) is float
v = fp.e1(1.0)
assert ae(v, 0.21938393439552027368, tol=ATOL)
assert type(v) is float
v = fp.e1(2.0)
assert ae(v, 0.048900510708061119567, tol=ATOL)
assert type(v) is float
v = fp.e1(5.0)


def test_fp_stress_ei_e1_1():
# Can be tightened on recent Pythons with more accurate math/cmath
ATOL = 1e-13
PTOL = 1e-12
v = fp.e1(1.1641532182693481445e-10)
assert ae(v, 22.296641293693077672, tol=ATOL)
assert type(v) is float
v = fp.e1(0.25)

    assert ae(v, 1.0442826344437381945, tol=ATOL)
assert type(v) is float
v = fp.e1(1.0)
assert ae(v, 0.21938393439552027368, tol=ATOL)
assert type(v) is float
v = fp.e1(2.0)
assert ae(v, 0.048900510708061119567, tol=ATOL)
assert type(v) is float
v = fp.e1(5.0)