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LetT n (x) be trigonometric polynomial of degreen, and be conjugation ofT n (x). In this paper we obtain the complete asymptotic expansion for

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$C_n = \mathop {\sup }\limits_{\left\| {T_n } \right\|C \leqslant 1} \left\| {\tilde T_n } \right\|_C$$ \end{document}
forn→∞.

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