Is the Wigner Ville transform implemented in Maple or its' Toolboxes?

I recently attempted to Fourier Transform the LommelS1 function using Maple. After loading

restart;
with(inttrans);
[addtable, fourier, fouriercos, fouriersin, hankel, hilbert, invfourier, invhilbert, invlaplace, invmellin, laplace, mellin,   savetable, setup]

the command did not work on LommelS1, after several attempts. I then used the 1F2 hypergeometric definition of LommelS1, and tried
fourier (t^(mu + 1)*hypergeom([1], [3/2 + nu/2 + mu/2, 3/2 - nu/2 + mu/2], -t^2/4)/((mu - nu + 1)*(mu + nu + 1)), t, w)

and after about 6 attempts of restart thru to fourier(...), it finally gave me about 30 lines of output, which simplified to about 8 lines, then subsequently simplified symbolically to two final lines of output- but I haven't been able to reproduce the result since (after about 20 attempts), so it really makes me question the algorithm, its implementation and its stability, or am I missing something here??

I want to convert the Chebyshev T(n,x) and U(n-1,x) polnomials into their inverse trigonometric definitions. Is there a simple conversion process available in Maple?  There is a command "invtrig" which I have tried with the "convert" command , but this does not seem to work.

I wrote a simple expand command in Maple - expand(cos((u - 2*k)*x))

only to get the result

2*cos(x*u)*cos(x*k)^2 + 2*sin(x*u)*sin(x*k)*cos(x*k) - cos(x*u)

The presence of a squared term seems to indicate a bug??

Is there a single-source fractional calculus toolbox, or collection of tools, available for Maple ? There appears to be the odd routine for fractional derivatives or DE's, but nothing of a systemic nature.