View source for T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n

==Theorem==
The following formula holds:
$$T_n(x)=\dfrac{\left(x+i\sqrt{1-x^2} \right)^n+\left(x-i\sqrt{1-x^2} \right)^n}{2},$$
where $T_n$ denotes [[Chebyshev T]] and $i$ denotes the [[imaginary number]].

==Proof==

==References==
* {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Chebyshev U|next=U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n}}: Theorem 7.1 (i)

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