# 1. Differential Equation[-]

The function $${L_{n}^{(l)}\left(x\right)}$$ satisfies the differential equation$$\displaystyle x{\frac {d^{2}}{d{x}^{2}}}y \left( x \right) + \left( l+1-x \right) {\frac {d}{dx}}y \left( x \right) +ny \left( x \right) = 0.$$
All formulas on this page are valid under the condition that $$l$$ is not an integer (special values for parameters can be entered at the bottom).

# 4. Local Expansions at Singularities and at Infinity[-]

The differential equation above has 0 non-zero finite .

# 6. Parameters[-]

The Laguerre function $${L_{n}^{(l)}\left(x\right)}$$ depends on the parameters $$n$$ and $$l$$. The boxes below can be used to rename or instantiate these parameters.
p1 =  p2 =