View source for Orthogonality of Chebyshev T on (-1,1)

==Theorem==
The following formula holds for $m,n \in \{0,1,2,\ldots\}$:
$$\int_{-1}^1 \dfrac{T_m(x)T_n(x)}{\sqrt{1-x^2}} \mathrm{d}x = \left\{ \begin{array}{ll}
0 &; m \neq n \\
\dfrac{\pi}{2} &; m=n\neq 0 \\
\pi &; m=n=0,
\end{array} \right.$$
where $T_m$ denotes [[Chebyshev T|Chebyshev polynomials of the first kind]].

==Proof==

==References==
* {{BookReference|An Introduction to Orthogonal Polynomials|1978|T.S. Chihara|prev=Orthogonality relation for cosine on (0,pi)|next=Chebyshev T}} $(1.3)$ (<i>note: only mentions the $m \neq n$ case</i>)

[[Category:Theorem]]
[[Category:Unproven]]