Complex Chebyshev polynomials on circular sectors with degree six or less
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 by U. Grothkopf and G. Opfer PDF
 Math. Comp. 39 (1982), 599615 Request permission
Abstract:
Let $T_n^\alpha$ denote the nth Chebyshev polynomial on the circular sector ${S^\alpha } = \{ z:z \leqslant 1,\arg z \leqslant \alpha \}$. This paper contains numerical values of ${\left \ {T_n^\alpha } \right \_\infty }$ and the corresponding coefficients of $T_n^\alpha$ for $n = 1(1)6$ and $\alpha = {0^ \circ }({5^ \circ }){180^ \circ }$. Also all critical angles for $T_n^\alpha ,n = 1(1)6$ are listed, where an angle is called critical when the number of absolute maxima of $T_n^\alpha $ changes at that angle. All figures are given to six places. The positions (and hence the number) of extremal points of $T_n^\alpha ,n = 1(1)6$ are presented graphically. The method consists of a combination of semiinfinite linear programming, finite linear programming, and Newton’s method.References

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Additional Information
 © Copyright 1982 American Mathematical Society
 Journal: Math. Comp. 39 (1982), 599615
 MSC: Primary 30E10; Secondary 65D20
 DOI: https://doi.org/10.1090/S00255718198206696522
 MathSciNet review: 669652