Tag Archives: divergent integrals

C.D. Tica and E.A. Galapon, “Finite-Part Integration of the Generalized Stieltjes Transform and its dominant asymptotic behavior for small values of the parameter” arXiv:1703.07979.

By | March 24, 2017
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The paper addresses the exact evaluation of the generalized Stieltjes transform about from which the asymptotic behavior of for small parameters is directly extracted. An attempt to evaluate the integral by expanding the integrand about and then naively integrating the resulting infinite series term by term lead to an infinite series whose terms are divergent… Read More »

Galapon EA. 2017 The problem of missing terms in term by term integration involving divergent integrals. Proc. R. Soc. A 473: 20160567.

By | January 20, 2017
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The operations of integration and summation cannot be interchanged arbitrarily. Some uniformity conditions must be satisfied in order for the interchange to be performed. If the conditions are not satisfied and the interchange is nevertheless carried out, some outrageous things happen. For example, the interchange may lead to an infinite series of divergent integrals; that… Read More »