Uma fórmula geral não recursiva da soma das funções polinomiais dos inteiros positivos

The main objective of this work is to present a non-recursive general formula that determines the sum of polynomial functions applied to positive integers. For this, some generalizations of the concept of functions and sequences using the higher-order difference operator are presented. Thus, with th...

Descripción completa

Detalles Bibliográficos
Autor: Sena, Francisco Adriano Maciel de Brito
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2021
País:Brasil
Institución:Universidade Federal Rural do Semi-Árido (UFERSA)
Repositorio:Repositório Digital da Universidade Federal Rural do Semi-Árido (RDU)
Idioma:portugués
OAI Identifier:oai:repositorio.ufersa.edu.br:prefix/7039
Acceso en línea:https://repositorio.ufersa.edu.br/handle/prefix/7039
Access Level:acceso abierto
Palabra clave:Funções polinomiais
Diferença finita
Operadores
Números de Bernoulli
Somas de potências de inteiros
Polynomial functions
Finite difference
Operators
Bernoulli numbers
Sums of integer powers
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Descripción
Sumario:The main objective of this work is to present a non-recursive general formula that determines the sum of polynomial functions applied to positive integers. For this, some generalizations of the concept of functions and sequences using the higher-order difference operator are presented. Thus, with this, we obtain a formula for the sum of the powers of non-negative integers, which is a particular case of polynomial functions. Then, a formula for determining the general term of a higher order arithmetic progression is obtained, as well as a formula for determining the sum of the first n terms of it. And finally, you get a formula to determine a figured number and the sum of them for whatever the number of sides