Add rewrite of 'li(z)' in terms of Meijer G functions

In [3]: li(z).rewrite(meijerg)
Out[3]: -log(1/log(z))/2 - log(-log(z)) + log(log(z))/2 - meijerg(((), (1,)), ((0, 0), ()), -log(z))

In [4]: pprint(_)
     ⎛  1   ⎞
  log⎜──────⎟
     ⎝log(z)⎠                  log(log(z))   ╭─╮2, 0 ⎛      1 │        ⎞
- ─────────── - log(-log(z)) + ─────────── - │╶┐     ⎜        │ -log(z)⎟
       2                            2        ╰─╯1, 2 ⎝0, 0    │        ⎠

In [5]: hyperexpand(_)
Out[5]: ((-log(log(z)*exp_polar(2*I*pi)) + Ei(log(z)) + 2*I*pi)/log(z) - EulerGamma/log(z))*log(z) + log(log(z)*exp_polar(I*pi)) - log(1/log(z))/2 - log(-log(z)) + log(log(z))/2 + EulerGamma

In [6]: pprint(_)
                                                                                        ⎛  1   ⎞
⎛     ⎛        2⋅ⅈ⋅π⎞                                  ⎞                             log⎜──────⎟
⎜- log⎝log(z)⋅ℯ     ⎠ + Ei(log(z)) + 2⋅ⅈ⋅π   EulerGamma⎟             ⎛        ⅈ⋅π⎞      ⎝log(z)⎠                  log(log(z))
⎜───────────────────────────────────────── - ──────────⎟⋅log(z) + log⎝log(z)⋅ℯ   ⎠ - ─────────── - log(-log(z)) + ─────────── + EulerGamma
⎝                  log(z)                      log(z)  ⎠                                  2                            2

In [7]: simplify(_)
Out[7]: -log(1/log(z))/2 - log(-log(z)) + log(log(z))/2 + Ei(log(z)) + I*pi

In [8]: pprint(_)
     ⎛  1   ⎞
  log⎜──────⎟
     ⎝log(z)⎠                  log(log(z))
- ─────────── - log(-log(z)) + ─────────── + Ei(log(z)) + ⅈ⋅π
       2                            2

In [9]: _.rewrite(li)
Out[9]: -log(1/log(z))/2 - log(-log(z)) + log(log(z))/2 + li(z) + I*pi

In [10]: pprint(_)
     ⎛  1   ⎞
  log⎜──────⎟
     ⎝log(z)⎠                  log(log(z))
- ─────────── - log(-log(z)) + ─────────── + li(z) + ⅈ⋅π
       2                            2

We have to see how we can get rid of those nested 'log's in front ...