T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n
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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
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 7.1 (i)
