Sidi, Avram; Lubinsky, Doron S. Biorthogonal polynomials and numerical integration formulas for infinite intervals. (English) Zbl 1221.65081 JNAIAM, J. Numer. Anal. Ind. Appl. Math. 2, No. 3-4, 209-226 (2007). The paper refers to a class of numerical quadrature formulas for the infinite-range integrals \(\int^\infty_0w(x)f(x)dx\), where \(w(x)=x^ae^{-x}\) or \(w(x)=x^a\int_1^\infty e^{-xt}t^{-p}dt\). Integrals \(\int^\infty_{\dot u}w(x)/(z-x)dx\) involving this \(w(x)\) arise in radiation theory. It is pointed out that these formulas are obtained by applying the Levin and Sidi transformations, effective convergence methods to the asymptotic expansions of \(\int^\infty_{\dot u}w(x)/(z-x) \,dx\) (see [A. Sidi, Math. Comput. 35, 851–874 (1980; Zbl 0441.41021)]). All that turns out to be interpolatory. The effectivness of the numerical quadrature formulas is shown in some tables. Reviewer: Vladimir N. Karpushkin (Moskva) Cited in 7 Documents MSC: 65D32 Numerical quadrature and cubature formulas 65D30 Numerical integration 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 33C47 Other special orthogonal polynomials and functions 40A25 Approximation to limiting values (summation of series, etc.) 41A20 Approximation by rational functions 41A55 Approximate quadratures 65B10 Numerical summation of series Keywords:biothogonal polynomials; convergence acceleration; numerical integration Citations:Zbl 0441.41021 PDFBibTeX XMLCite \textit{A. Sidi} and \textit{D. S. Lubinsky}, JNAIAM, J. Numer. Anal. Ind. Appl. Math. 2, No. 3--4, 209--226 (2007; Zbl 1221.65081)