- Goncharov, V. L. (2000). [The theory of best approximation of
   functions.](https://www.sciencedirect.com/science/article/pii/S0021904500934762) Journal of Approximation Theory, 106(1), 2-57.

Gonchorov discussing historically approximation theory contains the following footnote:

[![Footnote crediting Bernstein's dissertation coining Tn the Chebyshev polynomial][1]][1]

Indeed the notation can be found in [Bernstein's 1913 dissertation](https://history-of-approximation-theory.com/fpapers/bernstein1913.pdf).

It is unclear when exactly $U_n$ was introduced. It appears, together with $T_n$ in Pólya, G., & Szegö, G. (1925). [Aufgaben und Lehrsätze aus der Analysis. Vol 2. Springer, p. 75.](https://link.springer.com/chapter/10.1007/978-3-662-38380-3_3) I do not know of an earlier source using this notation. I suspect that the notation was introduced into the English literature via Szegö (1939) Orthogonal Polynomials, AMS.

Incidentally the introduction of the Chebyshev polynomial of the second kind is credited to Korkin and Zolotarev (1873) by Steffens, K. G. (2006) [The history of approximation theory: from Euler to Bernstein](https://link.springer.com/book/10.1007/0-8176-4475-X), Birkhäuser, p. 92.

  [1]: https://i.sstatic.net/iVxxNwbj.png