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• Goncharov, V. L. (2000). The theory of best approximation of functions. Journal of Approximation Theory, 106(1), 2-57.

Gonchorov discussing historically approximation theory contains the following footnote:

Indeed the notation can be found in Bernstein's 1913 dissertation (see page 52):

Conifold provided the following translation for the bottom paragraph via google translate:

For brevity we will in the following call c.$T_n(x)$, where c is a constant, trigonometric polynomials, and derive some of their properties, analogous to the property, discovered by Chebyshev.

Conifold hence rightly points out that for Berinstein "T" apparently is for trigonometric. Hence for Bernstein it was not a variant of Tchebychef that has since become an oft repeated explanation for the letter (compare Rivlin (1974) The Chebyshev Polynomials. p. 4. and Mason and Handscomb (2003) Chebyshev Polynomials. Appendix A). To be sure the current attribution is helpful in the context of orthogonal polynomial classification as they, in general, are attributed to a name (compare Abramowitz & Stegun (1965) p. 774f.).

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. 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, Birkhäuser, p. 92.

• Goncharov, V. L. (2000). The theory of best approximation of functions. Journal of Approximation Theory, 106(1), 2-57.

Gonchorov discussing historically approximation theory contains the following footnote:

Indeed the notation can be found in Bernstein's 1913 dissertation (see page 52):

Conifold provided the following translation for the bottom paragraph via google translate:

For brevity we will in the following call c.$T_n(x)$, where c is a constant, trigonometric polynomials, and derive some of their properties, analogous to the property, discovered by Chebyshev.

Conifold hence rightly points out that for Bernstein "T" apparently is for trigonometric. Hence for Bernstein it was not a variant of Tchebychef that has since become an oft repeated explanation for the letter (compare Rivlin (1974) The Chebyshev Polynomials. p. 4. and Mason and Handscomb (2003) Chebyshev Polynomials. Appendix A). To be sure the current attribution is helpful in the context of orthogonal polynomial classification as they, in general, are attributed to a name (compare Abramowitz & Stegun (1965) p. 774f.).

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. 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, Birkhäuser, p. 92.

• Goncharov, V. L. (2000). The theory of best approximation of functions. Journal of Approximation Theory, 106(1), 2-57.

Gonchorov discussing historically approximation theory contains the following footnote:

Indeed the notation can be found in Bernstein's 1913 dissertation (see page 52):

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. 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, Birkhäuser, p. 92.

• Goncharov, V. L. (2000). The theory of best approximation of functions. Journal of Approximation Theory, 106(1), 2-57.

Gonchorov discussing historically approximation theory contains the following footnote:

Indeed the notation can be found in Bernstein's 1913 dissertation (see page 52):

Conifold provided the following translation for the bottom paragraph via google translate:

For brevity we will in the following call c.$T_n(x)$, where c is a constant, trigonometric polynomials, and derive some of their properties, analogous to the property, discovered by Chebyshev.

Conifold hence rightly points out that for Berinstein "T" apparently is for trigonometric. Hence for Bernstein it was not a variant of Tchebychef that has since become an oft repeated explanation for the letter (compare Rivlin (1974) The Chebyshev Polynomials. p. 4. and Mason and Handscomb (2003) Chebyshev Polynomials. Appendix A). To be sure the current attribution is helpful in the context of orthogonal polynomial classification as they, in general, are attributed to a name (compare Abramowitz & Stegun (1965) p. 774f.).

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. 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, Birkhäuser, p. 92.

• Goncharov, V. L. (2000). The theory of best approximation of functions. Journal of Approximation Theory, 106(1), 2-57.

Gonchorov discussing historically approximation theory contains the following footnote:

Indeed the notation can be found in Bernstein's 1913 dissertation.

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. 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, Birkhäuser, p. 92.

• Goncharov, V. L. (2000). The theory of best approximation of functions. Journal of Approximation Theory, 106(1), 2-57.

Gonchorov discussing historically approximation theory contains the following footnote:

Indeed the notation can be found in Bernstein's 1913 dissertation (see page 52):

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. 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, Birkhäuser, p. 92.