Chebyshev Polynomials
We use Euler's formula to express cos(nx) and sin(nx) as polynomials in cos(x) or sin(x) respectively. The relationship cos(nx) = T_n(cos(x)) defines a sequence of polynomials known as the Chebyshev polynomials which arise in numerical analysis. We find the first few Chebyshev polynomials of the first kind and derive a recursion relationship for them. We find the second order ODE which these polynomials statisfy in this video: • Chebyshev's Differential Equation and...
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