Definition:Laguerre's Differential Equation/Laguerre Polynomial
< Definition:Laguerre's Differential Equation(Redirected from Definition:Laguerre Polynomial)
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Definition
The Laguerre polynomials are the solutions to Laguerre's differential equation:
- $x \dfrac {\d^2 y} {\d x^2} + \paren {1 - x} \dfrac {\d y} {\d x} + \alpha y = 0$
for $\alpha = n$.
They are of the form:
- $\map {L_n} x = e^x \map {\dfrac {\d^n} {\d x^n} } {x^n e^{-x} }$
Also see
- Results about Laguerre polynomials can be found here.
Source of Name
This entry was named for Edmond Nicolas Laguerre.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Laguerre's differential equation
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Laguerre's differential equation