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...
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| 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 |
| 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 |
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