Definition:Chebyshev Polynomials/Second Kind

Definition
The Chebyshev polynomials of the second kind are defined as polynomials such that:

Recursive Definition

 * $\map {U_n} x = \begin{cases}

1 & : n = 0 \\ 2 x & : n = 1 \\ 2 x \map {U_{n - 1} } x - \map {U_{n - 2} } x & : n > 1 \end{cases}$

Also see

 * Existence of Chebyshev Polynomials of the Second Kind where its existence is demonstrated.
 * Definition:Chebyshev Polynomials of the First Kind