Updates:
Cc: -ness...@googlemail.com
Comment #10 on issue 3057 by someb...@bluewin.ch: Closed form results for
meijerg functions
http://code.google.com/p/sympy/issues/detail?id=3057
Again, hyperexpand works now, but results are different:
In [34]: sympify("meijerg(((1/2, 0), ()), ((1/2, 0, 0), (1/2,)),
a**2*w**2/4)")
Out[34]: meijerg(((1/2, 0), ()), ((1/2, 0, 0), (1/2,)), a**2*w**2/4)
In [35]: pprint(_)
⎛ │ 2 2⎞
╭─╮3, 2 ⎜ 1/2, 0 │ a ⋅w ⎟
│╶┐ ⎜ │ ─────⎟
╰─╯2, 4 ⎝1/2, 0, 0 1/2 │ 4 ⎠
In [36]: hyperexpand(_)
Out[36]: -sqrt(pi)*(2*(Si(a*w) - pi/2)*sin(a*w) + 2*cos(a*w)*Ci(a*w))
In [37]: simplify(_)
Out[37]: -sqrt(pi)*((2*Si(a*w) - pi)*sin(a*w) + 2*cos(a*w)*Ci(a*w))
In [38]: pprint(_)
___
-╲╱ π ⋅((2⋅Si(a⋅w) - π)⋅sin(a⋅w) + 2⋅cos(a⋅w)⋅Ci(a⋅w))
In [39]: cosine_transform(1/(a+t), t, w)
Out[39]: -sqrt(2)*((2*Si(a*w) - pi)*sin(a*w)/2 + cos(a*w)*Ci(a*w))/sqrt(pi)
In [40]: simplify(_)
Out[40]: -sqrt(2)*((2*Si(a*w) - pi)*sin(a*w)/2 + cos(a*w)*Ci(a*w))/sqrt(pi)
In [41]: pprint(_)
___ ⎛(2⋅Si(a⋅w) - π)⋅sin(a⋅w) ⎞
-╲╱ 2 ⋅⎜──────────────────────── + cos(a⋅w)⋅Ci(a⋅w)⎟
⎝ 2 ⎠
────────────────────────────────────────────────────
___
╲╱ π
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