Chebyshev Polynomial Calculator (Tₙ, Uₙ)
Evaluate Chebyshev polynomials of the first and second kind, list their coefficients and roots.
How to use the Chebyshev Polynomial Calculator
- Enter or select: Degree n, Argument x.
- The results (Tₙ(x), Uₙ(x), Tₙ coefficients (x⁰ … xⁿ), Roots of Tₙ) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- T₀=1, T₁=x, Tₙ₊₁ = 2x·Tₙ − Tₙ₋₁
- Tₙ(cos θ) = cos(nθ)
- Roots: cos((2k−1)π/2n)
About this tool
Chebyshev polynomials are the basis of equiripple filters and Dolph–Chebyshev antenna arrays.