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laguer

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There are 6 letters in LAGUER ( A1E1G2L1R1U1 )

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Definitions of laguer in various dictionaries:

LAGUER - In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 - 1886), are solutions of Laguerre's equation: x ...

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Laguer might refer to
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 - 1886), are solutions of Laguerre's equation:*
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* {\displaystyle xy''+(1-x)y'+ny=0}
* which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer.
* Sometimes the name Laguerre polynomials is used for solutions of
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* {\displaystyle xy''+(\alpha +1-x)y'+ny=0~.}
* where n is still a non-negative integer.
* Then they are also named generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor Nikolay Yakovlevich Sonin).
* 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
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* {\displaystyle \int _{0}^{\infty }f(x)e^{-x}\,dx.}
* These polynomials, usually denoted L0, L1, ..., are a polynomial sequence which may be defined by the Rodrigues formula,
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