Complex Chebyshev polynomials on circular sectors with degree six or less
Authors:
U. Grothkopf and G. Opfer
Journal:
Math. Comp. 39 (1982), 599615
MSC:
Primary 30E10; Secondary 65D20
DOI:
https://doi.org/10.1090/S00255718198206696522
MathSciNet review:
669652
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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.

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© Copyright 1982
American Mathematical Society