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Gives the Dirichlet eta function, `\eta(s)`, also known as the
alternating zeta function. This function is defined in analogy
with the Riemann zeta function as providing the sum of the
alternating series

.. math ::

    \eta(s) = \sum_{k=0}^{\infty} \frac{(-1)^k}{k^s}
        = 1-\frac{1}{2^s}+\frac{1}{3^s}-\frac{1}{4^s}+\ldots
(more...)

src/s/y/sympy-0.7.5/sympy/mpmath/tests/test_fp.py   sympy(Download)
    assert ae(fp.zeta(32.7), 1.0000000001433243232)
    assert ae(fp.zeta(100), 1.0)
    assert ae(fp.altzeta(3.5), 0.92755357777394803511)
    assert ae(fp.altzeta(1), 0.69314718055994530942)
    assert ae(fp.altzeta(2), 0.82246703342411321824)
    assert ae(fp.altzeta(0), 0.5)

src/s/y/sympy-HEAD/sympy/mpmath/tests/test_fp.py   sympy(Download)
    assert ae(fp.zeta(32.7), 1.0000000001433243232)
    assert ae(fp.zeta(100), 1.0)
    assert ae(fp.altzeta(3.5), 0.92755357777394803511)
    assert ae(fp.altzeta(1), 0.69314718055994530942)
    assert ae(fp.altzeta(2), 0.82246703342411321824)
    assert ae(fp.altzeta(0), 0.5)

src/s/y/sympy-polys-HEAD/sympy/mpmath/tests/test_fp.py   sympy-polys(Download)
    assert ae(fp.zeta(32.7), 1.0000000001433243232)
    assert ae(fp.zeta(100), 1.0)
    assert ae(fp.altzeta(3.5), 0.92755357777394803511)
    assert ae(fp.altzeta(1), 0.69314718055994530942)
    assert ae(fp.altzeta(2), 0.82246703342411321824)
    assert ae(fp.altzeta(0), 0.5)