M3: Laguerre Polynomials

The Laguerre polynomials are solutions of Laguerre's differential equation:

\[x\,y'' + (1 - x)\,y' + n\,y = 0\,\]

These are the first few Laguerre polynomials:

\(n\)	\(L_n(x)\,\)
0	1
1	\(-x+1\,\)
2	\({\frac{1}{2}} (x^2-4x+2) \,\)
3	\({\frac{1}{6}} (-x^3+9x^2-18x+6) \,\)
4	\({\frac{1}{24}} (x^4-16x^3+72x^2-96x+24) \,\)
5	\({\frac{1}{120}} (-x^5+25x^4-200x^3+600x^2-600x+120) \,\)
6	\({\frac{1}{720}} (x^6-36x^5+450x^4-2400x^3+5400x^2-4320x+720) \,\)