The Special Function {L_{n}^{(l)}\left(x\right)}


1. Differential Equation[-]

The function {L_{n}^{(l)}\left(x\right)} satisfies the differential equation
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).

2. Derivative in Terms of Lower-Order Derivatives[+]

3. Expansion at 0[+]

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

The differential equation above has 0 non-zero finite singular pointsA complex numberĀ z_0 is a singular point (or singularity of a linear ordinary differential equation with polynomial coefficients, if the leading coefficient of the equation vanishes atĀ z_0..

4.1. Expansion at \infty [+]

5. Hypergeometric Representation[+]

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 =