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...

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...