about the Laguerre square expansion Sin(x)

The following functional series are developments using Laguerre polynomials, the second is the square of the Laguerre polynomial, the first is half as fast as the second being this is the square of the Laguerre polynomial, this being non-orthogonal
How is this possible??
$$sin (x z)=sum _{n=0}^{infty } frac{1}{2} (-1)^n i^n z^n left(z^2+1right)^{-n-1} left((z-i) (1+i z)^n+(-1)^n (z+i) (1-i z)^nright) L_n(x)$$
$$frac{sin (x z)}{x z}=sum _{n=0}^{infty } frac{(L_n^{alpha }(x) L_n^{alpha }(-x)) left((-1)^{2 n} z^{2 n} Gamma (n+1)^2 , _3F_2left(n+frac{alpha }{2}+frac{1}{2},n+frac{alpha }{2}+1,n+alpha +1;n+frac{3}{2},2 n+alpha +2;-z^2right)right)}{Gamma (2 n+2)}$$