1. In a recent post I wanted to use a capital tau ... and so typed \mathcal{ \Tau_1 } but generated an error ...

I wanted the capital tau symbol as in the following text ...

Hope someone can help ...

Peter

2.

3. Hi Peter,

Capital Tau is just a T.
Mathjax doesn't have a caligraphic Tau, but the caligraphic T is the same thing: $\mathcal{T(S)}$.
Alternatively we can consider mathscr T: $\mathscr{T(S)}$.

I think that the T in your text is just a caligraphic T. It is just rendered slightly differently.
Note that a lowercase tau actually has its bottom curve in the opposite direction

although this is hardly visible in the mathjax version ($\tau$).

4. Try mathcal{T}, which gives $\displaystyle \mathcal{T}$.