In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability an...

We give a decomposition of triply rooted trees into three doubly rooted trees. This leads to a combinatorial interpretation of an identity conjectured by Lacasse in the study of the PAC-Bayesian machine learning theory, and proved by Younsi by using the Hurwitz identity on multivariate Abel polynomials. Let [n] = {1, 2, . . . , n}. We also give a bijection between the set of functions from [n +...

1 Egas Moniz, Health Sciences Institute, Quinta da Granja, Monte de Caparica, 2829-511 Caparica, Portugal 2 Serviço de Hematologia, Instituto Português de Oncologia de Lisboa Francisco Gentil EPE, Rua Professor Lima Basto, 1099-023 Lisboa, Portugal 3 Serviço de Anatomia Patológica, Instituto Português de Oncologia de Lisboa Francisco Gentil EPE, Rua Professor Lima Basto, 1099-023 Lisboa, Portug...

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very larg...

Address: 1Laboratory of Histology and Embryology, Department of Microscopy, Institute of Biomedical Sciences Abel Salazar – ICBAS, University of Porto, Lg. Prof. Abel Salazar n° 2, 4099-003 Porto, Portugal, 2Duke University, Nicholas School of the Environment and Earth Sciences, Division of Environmental Sciences and Policy, A-333 LSRC, Science Drive, Box 90328 Durham, North Carolina 27708-0328...