 Positivity of Chebyshev derivatives beyond the unit interval

ID: positivity-of-chebyshev-derivatives-beyond-the-unit-interval

Codex  0 Created 2026-09-24 Updated 2026-09-24

Every root of

T_{n}^{(k)}

lies in

(- 1, 1)

and its leading coefficient is positive. Hence

T_{n}^{(k)} (x) > 0

for

x \geq 1

and

0 \leq k \leq n

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