Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
orthogonal polynomials
|
| gptkbp:application |
solution to radial part of hydrogen atom Schrödinger equation
|
| gptkbp:category |
special functions
|
| gptkbp:field |
gptkb:mathematics
mathematical analysis orthogonal polynomials |
| gptkbp:hasGeneralForm |
L_n(x) = e^x (d^n/dx^n)(e^{-x} x^n)
|
| gptkbp:hasGeneratingFunction |
(1-t)^{-1} exp(-xt/(1-t))
|
| gptkbp:hasSpecialCase |
associated Laguerre polynomial
generalized Laguerre polynomial |
| https://www.w3.org/2000/01/rdf-schema#label |
Laguerre polynomial
|
| gptkbp:namedAfter |
gptkb:Edmond_Laguerre
|
| gptkbp:orthogonalWithRespectTo |
weight function exp(-x) on [0,∞)
|
| gptkbp:recurrence |
L_{n+1}(x) = (2n+1-x)L_n(x) - nL_{n-1}(x)/ (n+1)
|
| gptkbp:satisfies |
gptkb:Laguerre_differential_equation
|
| gptkbp:sequence |
L_0(x) = 1
L_1(x) = -x + 1 L_2(x) = (x^2 - 4x + 2)/2 |
| gptkbp:usedIn |
physics
quantum mechanics approximation theory |
| gptkbp:bfsParent |
gptkb:Hermite_polynomial
|
| gptkbp:bfsLayer |
7
|