We use the theory of orthogonal polynomials to write down explicit expressions for the polynomials of the first and second kind associated with a given infinite symmetric tridagonal matrix H. The Green's function is the inverse of the infinite symmetric tridiagonal matrix (H - zI). By calculating the inverse of the finite symmetric tridiagonal matrix (H-PP -- ZI(PP)) we can find the analytical form of the inverse of the finite symmetric tridiagonal matrix, H-PP. [References: 7]
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