? laguerre;

Calculate

? laguerre;

Calculate

### laguerre

Run Example
```(%i1)? gen_laguerre;

-- Function: gen_laguerre (<n>, <a>, <x>)
The generalized Laguerre polynomial of degree <n>.

Reference: Abramowitz and Stegun, equation 22.5.54, page 780.

(%o1)                                true
(%i2) ```
Run Example
```n:4;
(%o1)                                  4
(%i2) f(x):=rat(gen_laguerre(n,1/4,x));
1
(%o2)                 f(x) := rat(gen_laguerre(n, -, x))
4
(%i3) g:f(a-x)+(-1)^(n+1)*f(a+x);
3        3        2
(64 a - 272) x  + (64 a  - 816 a  + 2652 a - 1989) x
(%o3)/R/    - ----------------------------------------------------
192
(%i4) s: part(solve(coeff(g,x,n-1),[a]), 1);
17
(%o4)                               a = --
4
(%i5) subst(rhs(s),lhs(s),g);
17 x
(%o5)                                ----
6
(%i6) ```
Run Example
```lag(n,alpha,x):=rat(%e^x*x^(-alpha)*diff(x^(n+alpha)*%e^(-x),x,n)/n!);
x  - alpha       n + alpha   - x
%e  x        diff(x          %e   , x, n)
(%o1) lag(n, alpha, x) := rat(-----------------------------------------)
n!
(%i2) nn:2;
(%o2)                                  2
(%i3) gen:_laguerre(nn,a,x);
(%o3)                         _laguerre(2, a, x)
(%i4) lag(nn,a,x);
2                    2
x  + (- 2 a - 4) x + a  + 3 a + 2
(%o4)/R/               ---------------------------------
2
(%i5) ```

### Related Help

Help for Laguerre