Chebyshev Circles Blueprint

1 Introduction ▶
2 Preliminaries ▶
3 Discrete Orthogonality Relations ▶
- 3.1 Sums of cosines at rotated roots
- 3.2 Chebyshev angle sums
4 Power Sum Invariance ▼
5 From Power Sums to Polynomial Coefficients ▶
- 5.1 Newton’s identities: the algebraic bridge
- 5.2 Why the constant term varies
6 Proof of Main Theorem ▶
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4.2 Computational examples

Before proving the general case, we illustrate the invariance with explicit calculations for small values.