Laguerre polynomials Totally Explained

Everything about Laguerre Polynomials totally explained

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

x,y

+ (1 - x),y' + n,y = 0, which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer.
These polynomials, usually denoted $L_0, L_1, dots$ , are a polynomial sequence which may be defined by the Rodrigues formula ť L_n(x)=frac ,_1F_1(-n,alpha+1,x)

where

(a)_n

is the Pochhammer symbol (which in this case represents the rising factorial).

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