Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXLIII, No. 36, pp. 1–19 (2011) 

Calculating a class of integrals encountered in theoretical chemistryI. Gutman and G. V. MilovanovicFaculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, SerbiaMegatrend University, Faculty of Computer Sciences, Bulevar umetnosti 29, 11070 Novi Beograd, Serbia Abstract: The methods for numerical calculating the Cauchy principal value integrals of the form $ {\displaystyle\mbox v.p. \int_{\infty}^{+\infty} }\logP(ix)/Q(ix) dx$ are developed, where $P(x)$ and $Q(x)$ are monic polynomials of equal degrees with integer coefficients, and $i=\sqrt{1}$ . These integrals play a distinguished role in theoretical chemistry. Keywords: Numerical integration, Cauchy principal value integral, rational function, double exponential transformation, Gaussian quadrature, Chebyshev weight function, weights, nodes, theory of cyclic conjugation, cyclic conjugation energy effect, chemistry Classification (MSC2000): 65D30, 92E10 Full text of the article: (for faster download, first choose a mirror)
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