Logo
Published on

Quick Chebyshev value

Authors
  • avatar
    Name
    Vu Hung
    Twitter

Problem Statement

For the second-kind Chebyshev polynomial

U2(x)=4x2−1,U_2(x)=4x^2-1,

find U2(12)U_2\left(\frac12\right).

Hints

Substitute x=12x=\frac12 carefully.

Solutions

U2(12)=4(14)−1=1−1=0.U_2\left(\frac12\right)=4\left(\frac14\right)-1=1-1=0.

Takeaways

  • For a given Chebyshev polynomial, direct substitution is often enough.
  • Square fractions before multiplying by the coefficient.

Further Readings

Connect with me