CAOP

Plot

ChebyshevT Polynomials

Definition

The ChebyshevT polynomials are defined as

\[ \begin{align} T_n(x) &= \frac{n}{2}\,\sum_{k=0}^{[n/2]} \frac{(-1)^k\,(n-k-1)!}{k!\,(n-2k)!}\,(2x)^{n-2k}\\ &= \frac{1}{2} (2x)^n {}_2F_1 \left(\left. {-n/2, -n/2+\frac{1}{2} \atop -n+1} \; \right| \frac{1}{x^2} \right) \end{align} \]

Differential Equation

Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

factor (use Maple-style input)

   hypergeometric term in \(n\) and hyperexponential term in \(x\) required