U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n
From specialfunctionswiki
Theorem
The following formula holds: $$U_n(x) =-\dfrac{i}{2} \left[ \left( x + i \sqrt{1-x^2} \right)^n + \left( x-i\sqrt{1-x^2} \right)^n \right],$$ where $U_n$ denotes Chebyshev U and $i$ denotes the imaginary number.
Proof
References
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 7.1 (ii)
