- #1
ognik
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Hi - does anyone know of a program library/subroutine/some other source, to find the zeros of a generalised Laguerre polynomial? ie. $ L^{\alpha}_N (x_i) = 0 $
LaguerreL[n,a,x]
The zeros of generalised Laguerre polynomial are the values of the variable that make the polynomial equal to zero. They are often referred to as roots.
The zeros of generalised Laguerre polynomial can be calculated using numerical methods such as the Newton-Raphson method or the bisection method. They can also be found by solving the polynomial analytically.
The zeros of generalised Laguerre polynomial have many applications in mathematics, physics, and engineering. They are used to solve differential equations, study quantum systems, and approximate functions, among others.
Yes, the zeros of generalised Laguerre polynomial can be complex numbers. In fact, in some cases, the polynomial may have only complex zeros. These complex zeros are often found in pairs, known as conjugate pairs.
Yes, the zeros of generalised Laguerre polynomial have some special properties. For example, they are symmetric with respect to the real axis and the number of zeros is equal to the degree of the polynomial. Moreover, the zeros are also related to the coefficients of the polynomial through certain recurrence relations.