We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found, illustrating the effectiveness of the proposed ap...

Copyright: © 2015 Pereira D, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. *Corresponding author: Daniel Pereira, Internal Medicine resident, Serviço de Medicina, Centro Hospitalar do Porto, Largo Pro...

In this paper we introduce new Tauberian conditions for Abel summability method that include Hardy Littlewood Tauberian condition [4] as a special case. Mathematics Subject Classification: 40E05

The basic necessary conditions for the existence of a (v, k, λ)-perfect Mendelsohn design (briefly (v, k, λ)-PMD) are v ≥ k and λv(v− 1) ≡ 0 (mod k). These conditions are known to be sufficient in most cases, but certainly not in all. For k = 3, 4, 5, 7, very extensive investigations of (v, k, λ)-PMDs have resulted in some fairly conclusive results. However, for k = 6 the results have been far ...

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...