Complex Chebyshev polynomials on circular sectors with degree six or less

Authors:
U. Grothkopf and G. Opfer

Journal:
Math. Comp. **39** (1982), 599-615

MSC:
Primary 30E10; Secondary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669652-2

MathSciNet review:
669652

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Abstract: Let denote the *n*th Chebyshev polynomial on the circular sector . This paper contains numerical values of and the corresponding coefficients of for and . Also all critical angles for are listed, where an angle is called critical when the number of absolute maxima of changes at that angle. All figures are given to six places. The positions (and hence the number) of extremal points of are presented graphically. The method consists of a combination of semi-infinite linear programming, finite linear programming, and Newton's method.

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0669652-2

Article copyright:
© Copyright 1982
American Mathematical Society