Ticket #12596: trac_12596.3.patch

File trac_12596.3.patch, 1.6 KB (added by benjaminfjones, 9 years ago)

removed trailing whitespace

  • sage/functions/special.py

    # HG changeset patch
    # User Benjamin Jones <benjaminfjones@gmail.com>
    # Date 1332822935 18000
    # Node ID bd2f350f96fc666f8caeef26dcee938463031227
    # Parent  66e568c3d082ee389659bd257efa500e5a8e5955
    Trac 12596: improve documentation for elliptic_pi: describe the parameters, add a doctest to illustrate
    
    
    diff --git a/sage/functions/special.py b/sage/functions/special.py
    a b  
    16221622
    16231623    .. math::
    16241624
    1625         \int_0^\phi \frac{dx}{(1 - n\sin(x)^2)\sqrt{1 -
    1626         m\sin(x)^2}}.
     1625        \text{elliptic\_pi}(n, t, m) = \int_0^t \frac{dx}{(1 - n \sin(x)^2)
     1626        \sqrt{1 - m \sin(x)^2}}.
     1627
     1628    INPUT:
     1629
     1630    - ``n`` -- a real number, called the "characteristic"
     1631
     1632    - ``t`` -- a real number, called the "amplitude"
     1633
     1634    - ``m`` -- a real number, called the "parameter"
    16271635
    16281636    EXAMPLES::
    16291637
     1638        sage: N(elliptic_pi(1, pi/4, 1))
     1639        1.14779357469632
     1640
     1641    Compare the value computed by Maxima to the definition as a definite integral
     1642    (using GSL)::
     1643
    16301644        sage: elliptic_pi(0.1, 0.2, 0.3)
    16311645        0.200665068221
     1646        sage: numerical_integral(1/(1-0.1*sin(x)^2)/sqrt(1-0.3*sin(x)^2), 0.0, 0.2)
     1647        (0.2006650682209791, 2.227829789769088e-15)
     1648
     1649    ALGORITHM:
     1650
     1651    Numerical evaluation and symbolic manipulation are provided by `Maxima`_.
     1652
     1653    REFERENCES:
     1654
     1655    - Abramowitz and Stegun: Handbook of Mathematical Functions, section 17.7
     1656      http://www.math.sfu.ca/~cbm/aands/
     1657    - Elliptic Functions in `Maxima`_
     1658
     1659    .. _`Maxima`: http://maxima.sourceforge.net/docs/manual/en/maxima_16.html#SEC91
    16321660    """
    16331661    def __init__(self):
    16341662        r"""