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The $n$-th Gauss-Laguerre quadrature scheme aims to approximate integral of exponentially decreassing function over $[0 ; \infty[$ by a finite sum, according to: $$ \int _0 ^{+ \infty} … Uspenksy, On the convergence of quadrature formulas related to an infinite interval, Trans. Amer. Math. …

Generally, a Gaussian quadrature of degree $n$ over an interval $I$ is defined so that it integrates exactly polynomials up to degree $2n - 1$. The main tool are the orthogonal polynomials. … For example, the space $\mathbb{R} \left [\dfrac{1}{X} \right ]$ could be useful to develop quadratures over $[1 ; + \infty[$, i.e. a quadrature rule $$ \int _1 ^{+ \infty} \omega(x) f(x) …

H., Secrest D., "Gaussian Quadrature Formulas". Prentice-Hall, Englewood Cliffs, N.J., 1966 gives some answer to my question. … .$$ In section 3.2.3 "Semi-infinite to Finite segment", a quadrature over $]0, 1]$ is construted to be exact for functions $$ t \longrightarrow \displaystyle { \sum _{k = 1} ^M a_k (\ln x)^k } \ .$$ …

In particular, I want to understand the error $\varepsilon_n(f)$ produced by the $n$-th degree Gauss-Laguerre quadrature. … Uspenksy, On the convergence of quadrature formulas related to an infinite interval, Trans. Amer. Math. …