How do you pronounce Laguerre polynomial?
How do you pronounce Laguerre polynomial?
- Phonetic spelling of Laguerre. la-guerre. lah-gair; French la-ger. la-gue-rre.
- Meanings for Laguerre.
- Translations of Laguerre. Japanese : ラゲー Chinese : 拉盖尔 Arabic : لأجير
What is Laguerre and legendre function?
The Legendre, Laguerre, and Hermite equations are all homogeneous second order Sturm-Liouville equations. In solving these equations explicit solutions cannot be found. That is solutions in in terms of elementary functions cannot be found. In many cases it is easier to find a numerical or series solution.
What is Laguerre equation?
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are solutions of Laguerre’s equation: which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer.
How do you spell Laguerre?
Ed·mond-Ni·co·las [ed-mawn-nee-kaw-lah], /ɛd mɔ̃ ni kɔˈlɑ/, 1834–86, French mathematician.
What are Laguerre polynomials used for?
Transverse mode, an important application of Laguerre polynomials to describe the field intensity within a waveguide or laser beam profile.
What are the associated Laguerre polynomials?
Solutions to the associated Laguerre Differential Equation with are called associated Laguerre polynomials . In terms of the normal Laguerre polynomials, The associated Laguerre polynomials are orthogonal over with respect to the Weighting Function . where is the Kronecker Delta. They also satisfy
When is a Laguerre function a solution?
More generally, a Laguerre function is a solution when n is not necessarily a non-negative integer. The Laguerre polynomials are also used for Gaussian quadrature to numerically compute integrals of the form
Is the Laguerre Ode orthogonal with scalar product?
The Laguerre ODE is not self-adjoint but can be brought to self-adjoint form by multiplication of Eq. (14.132) by e – x. The Ln are therefore orthogonal with scalar product because xe – x is the coefficient of y ″ after the multiplication by e – x and [Ln(x)L ′ m(x) – L ′ n(x)Lm(x)]xe – x ∣ ∞0 = 0.
Does the associated Laguerre expansion converge at t = 0?
The associated Laguerre expansion does converge, but Hile shows that its behavior at t = 0 is incorrect. Even so Hile’s implementation of the associated Laguerre expansion for f ( t) appears to converge slightly faster than Laguerre for up to three terms considered.
