Final answer:
The generating function for the generalized Laguerre polynomial can be expressed as (1 - x)^-α e^(x/2) d^n / dx^n (x^(n + α) e^(-x/2))
Step-by-step explanation:
The generating function for the generalized Laguerre polynomial can be expressed as:
Lnα(x) = (1 - x)-α ex/2 dn / dxn (xn + α e-x/2)
This generating function can be used to find the coefficients of the Laguerre polynomial by expanding it in a Taylor series.