Status: Accepted
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Labels: Type-Defect Priority-Medium
New issue 3055 by [email protected]: Simplification of bessel functions
http://code.google.com/p/sympy/issues/detail?id=3055
Some simplifications for the Bessel functions are missing.
An example:
cosine_transform(1/t*sin(a/t), t, w)
gives a huge, ugly result involving Bessel function I and J of small
integer order.
The answer given in Bronstein is \pi/2 J_0(2\sqrt{a \omega}) which contains
just
a single J_0. Our current answer has sums of J_2 and I_2, J_1 and I_1 and
J_0 and I_0.
There are also formulae for expanding Bessel functions of rational
order under the conditions that for the order it holds that:
n - 1/2 \in Z : half-integer values
n - 1/3 \in Z : one-third integer values
n - 2/3 \in Z : two-third integer values
We should implement these too. But as the result in not necessarily simpler,
maybe they should be used by 'expand_func' but not by 'besselsimp'.
Further the current implementation of the Bessel functions
do not have the various symmetry properties. For example we
can transform 'besselj(-n, x)' to get rid of the '-n'.
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