Polynomials of the form :
$ T_n(x) =2^{-1} \cdot ((x+\sqrt {x^2-1})^n+ (x-\sqrt {x^2-1})^n)$
are known as Chebyshev polynomials of the first kind .
Consider the polynomials of the form :
$P_n(x)=2^{-n} \cdot ((x+\sqrt {x^2-4})^n+ (x-\sqrt {x^2-4})^n)$
Have these polynomials some special name ?
First few polynomials of this form are :
$P_0(x) = 2$
$P_1(x) = x$
$P_2(x) =x^2- 2$
$P_3(x) =x^3-3x$
$P_4(x) = x^4-4x^2+2$
$\vdots$