RT Conference Proceedings
T1 Using extensions of the residue theorem for improper integrals computations with CAS
A1 Galán-García, José Luis
A1 Aguilera-Venegas, Gabriel
A1 Rodríguez-Cielos, Pedro
A1 Galán-García, María Ángeles
A1 Padilla-Domínguez, Yolanda Carmen
A1 Atencia-McKillop, Iván
A1 Rodríguez-Cielos, Ricardo
K1 Matemáticas computacionales
AB The computation of improper integrals of the  rst kind (integrals on unbounded domain) areused in di erent applications in Engineering (for example in Kynetic Energy, electric potential,probability density functions, Gamma and Beta functions, Laplace and FourierTransforms, Di erential Equations, . . . ). Nowadays, Computer Algebra Systems (CAS) arebeing used for developing such computations. But in many cases, some CAS lack of theappropriate rules for computing some of these improper integrals.In a previous talk in ESCO 2016 and a later extension, we introduced new rules forcomputing improper integrals of the  rst kind using some results from Advanced CalculusTheories (Residue Theorem, Laplace and Fourier Transforms) aimed to improve CAS capabilitieson this topic. In this talk, we develop new rules for computing other types of improperintegrals using different applications from extended versions of the Residue Theorem. We will show some examples of such improper integrals that current CAS can not compute.Using extensions of the Residue Theorem in Complex Analysis, we will be able to developnew rules schemes for these improper integrals. These new rules will improve the capabilitiesof CAS, making them able to compute more improper integrals.
YR 2018
FD 2018-06-14
LK https://hdl.handle.net/10630/15965
UL https://hdl.handle.net/10630/15965
LA spa
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 3 mar 2026