Status: Accepted
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Labels: Type-Defect Priority-Medium
New issue 3056 by [email protected]: Closed-form results of sums of
meijerg functions
http://code.google.com/p/sympy/issues/detail?id=3056
Sometimes the sum of two or more meijerg functions should simplify.
The functions usually differ only in the argument. Simplification
does not happen as long as we do/can not combine the functions.
The following examples come from various integral transforms:
fourier_transform(1/(2*a)*exp(-a*Abs(t)), t, w)
The sum should simplify:
meijerg(((1/2,), ()), ((1/2, 0, 1/2), ()), a**2*t**2*exp_polar(-I*pi)/4) +
meijerg(((1/2,), ()), ((1/2, 0, 1/2), ()), a**2*t**2*exp_polar(I*pi)/4)
Another one:
fourier_transform(1/(t**2+a**2), t, w)
where
meijerg(((1/2,), ()), ((1/2, 0, 1/2), ()),
pi**2*a**2*w**2*exp_polar(-I*pi)) + meijerg(((1/2,), ()), ((1/2, 0, 1/2),
()), pi**2*a**2*w**2*exp_polar(I*pi))
should simplify. (Each of those transformations has a very simple closed
form result.)
There are even more examples of the very same kind in the
sine/cosine/Fourier transform notebooks.
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