Seminário de Avaliação - Série A: Successive Operations with Real Variable Applied to Representing Special Functions and Computational Modeling

Orientadores:
Gilson Antônio Giraldi - Laboratório Nacional de Computação Científica - LNCC
José Karam Filho - Laboratório Nacional de Computação Científica - LNCC

Banca Examinadora:
Gilson Antônio Giraldi - Laboratório Nacional de Computação Científica - LNCC (presidente)
Renato Portugal - Laboratório Nacional de Computação Científica - LNCC
Abimael Fernando Dourado Loula - Laboratório Nacional de Computação Científica - LNCC
Carlile Campos Lavor - Universidade Estadual de Campinas - IMECC/UNICAMP
Franklin de Lima Marquezino - Universidade Federal do Rio de Janeiro - UFRJ/COPPE

Suplentes:
Alexandre Loureiro Madureira - Laboratório Nacional de Computação Cientí fica - LNCC

Resumo:

Successive products are functions that were first developed and applied to solve recursive equations, also indexed by integers [1]-[3]. In this thesis, significant advances are reached, expanding this concept and its applications. For convenience, the work has been subdivided into two units. In a nutshell, the first unit proposes an extension of successive products from the integer to the real domain with a new recursive system of equations and establishes the methodology to solve them. The second unit is markedly different when introducing and applying the concept of successive products as an abstract operator. This change in the perspective significantly simplifies the use of the framework, facilitating the demonstration of new properties of successive products. Besides, elimination ofambiguity and remarkable integration of the successive products framework with other tools are other advantages also reached. In both units mathematical applications are pre sented, for especial functions representation in the first unit, and for populational modeling in the second one, [4]-[5]. In the next steps, it is intended to represent other especial functions and to consider variable properties in the populational models.