Did I find the right examples for you? yes no      Crawl my project      Python Jobs

All Samples(1)  |  Call(1)  |  Derive(0)  |  Import(0)
Gives the Gauss hypergeometric function `\,_2F_1` (often simply referred to as
*the* hypergeometric function), defined for `|z| < 1` as

.. math ::

    \,_2F_1(a,b,c,z) = \sum_{k=0}^{\infty}
        \frac{(a)_k (b)_k}{(c)_k} \frac{z^k}{k!}.

and for `|z| \ge 1` by analytic continuation, with a branch cut on `(1, \infty)`
when necessary.(more...)

src/s/y/sympy-0.7.5/sympy/mpmath/tests/test_levin.py   sympy(Download)
  f = lambda n: mp.rf(2 / mp.mpf(3), n) * mp.rf(4 / mp.mpf(3), n) * z**n / (mp.rf(1 / mp.mpf(3), n) * mp.fac(n))
  v = mp.nsum(f, [0, mp.inf], method = "levin", steps = [10 for x in xrange(1000)])
  exact = mp.hyp2f1(2 / mp.mpf(3), 4 / mp.mpf(3), 1 / mp.mpf(3), z)
  assert abs(exact - v) < eps