where z = 2 λ e − ( x − x e ) ; N n = [ n ! ( 2 λ − 2 n − 1 ) Γ ( 2 λ − n ) ] 1 2 {\displaystyle z=2\lambda e^{-\left(x-x_{e}\right)}{\text{; }}N_{n}=\left[{\frac {n!\left(2\lambda -2n-1\right)}{\Gamma (2\lambda -n)}}\right]^{\frac {1}{2}}} and L n ( α ) ( z ) {\displaystyle L_{n}^{(\alpha )}(z)} is a generalized Laguerre polynomial: