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

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Calculating a class of integrals encountered in theoretical chemistry

I. Gutman and G. V. Milovanovic

Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia
Megatrend 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} }\log|P(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

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Electronic fulltext finalized on: 9 Oct 2011. This page was last modified: 8 Apr 2013.

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