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Evaluates the Riemann R function, a smooth approximation of the
prime counting function `\pi(x)` (see :func:`~mpmath.primepi`). The Riemann
R function gives a fast numerical approximation useful e.g. to
roughly estimate the number of primes in a given interval.

The Riemann R function is computed using the rapidly convergent Gram
series,

.. math ::
(more...)

src/s/y/sympy-0.7.5/sympy/mpmath/tests/test_fp.py   sympy(Download)
    assert ae(fp.primezeta(2.5+4j), (-0.16922458243438033385 - 0.010847965298387727811j))
    assert ae(fp.primezeta(4), 0.076993139764246844943)
    assert ae(fp.riemannr(3.7), 2.3034079839110855717)
    assert ae(fp.riemannr(8), 3.9011860449341499474)
    assert ae(fp.riemannr(3+4j), (2.2369653314259991796 + 1.6339943856990281694j))

src/s/y/sympy-HEAD/sympy/mpmath/tests/test_fp.py   sympy(Download)
    assert ae(fp.primezeta(2.5+4j), (-0.16922458243438033385 - 0.010847965298387727811j))
    assert ae(fp.primezeta(4), 0.076993139764246844943)
    assert ae(fp.riemannr(3.7), 2.3034079839110855717)
    assert ae(fp.riemannr(8), 3.9011860449341499474)
    assert ae(fp.riemannr(3+4j), (2.2369653314259991796 + 1.6339943856990281694j))

src/s/y/sympy-polys-HEAD/sympy/mpmath/tests/test_fp.py   sympy-polys(Download)
    assert ae(fp.primezeta(2.5+4j), (-0.16922458243438033385 - 0.010847965298387727811j))
    assert ae(fp.primezeta(4), 0.076993139764246844943)
    assert ae(fp.riemannr(3.7), 2.3034079839110855717)
    assert ae(fp.riemannr(8), 3.9011860449341499474)
    assert ae(fp.riemannr(3+4j), (2.2369653314259991796 + 1.6339943856990281694j))