"Verify Laguerre polynomials" -- use eval to substitute arbitrary expression x for y (y is a local var) L(x,n,a,y) = eval(exp(y) / (y^a n!) d(y^(n + a) exp(-y), y, n), y, x) for(n, 1, 3, y = L(x,n,a), check(x d(y,x,x) + (a + 1 - x) d(y,x) + n y == 0) ) -- for integer a (k is a local var) L(x,n,a,k) = (n + a)! sum(k, 0, n, (-x)^k / ((n - k)! (a + k)! k!)) for(n, 1, 3, for(a, 0, n - 1, y = L(x,n,a), check(x d(y,x,x) + (a + 1 - x) d(y,x) + n y == 0) )) "ok" Run