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De las sumas de potencias a las sucesiones de Appell y su caracterización a través de funcionales.
| dc.contributor.advisor | Carrillo Torres, Sergio Alejandro | spa |
| dc.contributor.author | Hurtado Benavides, Miguel Ángel | spa |
| dc.date.accessioned | 2021-09-21T23:39:28Z | spa |
| dc.date.available | 2021-09-21T23:39:28Z | spa |
| dc.date.created | 2020 | spa |
| dc.date.issued | 2020 | spa |
| dc.identifier.citation | Hurtado Benavides, Miguel Ángel. (2020). De las sumas de potencias a las sucesiones de Appell y su caracterización a través de funcionales. [Tesis de maestría]. Universidad Sergio Arboleda. | spa |
| dc.identifier.uri | http://hdl.handle.net/11232/1743 | eng |
| dc.description.abstract | El estudio de las sumas de potencias de enteros positivos ha sido un tema de interés desde la antigüedad [8] que se mantiene vigente hasta nuestros días, ver por ejemplo [29, 24]. Actualmente estas fórmulas son de conocimiento común, sobre todo para potencias bajas, y las encontramos como ejemplos sencillos de inducción matemática y de introducción a la integral de Riemann. Históricamente, existen evidencias de su desarrollo desde la escuela pitagórica, pero fue hasta el siglo XVII que Jacob Bernoulli [9, 10], motivado por investigaciones en probabilidad, quien alcanzó el triunfo de descifrar una fórmula general de tipo polinomial para cualquier potencia. Su método llevó además al descubrimiento de la sucesión de números que hoy llevan su nombre, a saber, los números de Bernoulli. Estos aparecen naturalmente en múltiples fórmulas del análisis matemático, por ejemplo como coeficientes en la expansión de Taylor de funciones trigonométricas y en el cálculo de sumas de series [32]. En efecto, ellos permiten el cálculo efectivo de (2k), donde k es un entero no nulo y denota la famosa función zeta de Riemann. | spa |
| dc.format.extent | 54 | spa |
| dc.format.mimetype | application/pdf | eng |
| dc.publisher | Universidad Sergio Arboleda | spa |
| dc.rights | https://repository.usergioarboleda.edu.co/bitstream/id/ece5f62c-2a67-4790-9a7d-aba331dcefca/license.txt | eng |
| dc.title | De las sumas de potencias a las sucesiones de Appell y su caracterización a través de funcionales. | spa |
| dc.subject.lemb | Sucesiones (Matemáticas) | spa |
| dc.subject.lemb | Polinomios | spa |
| dc.subject.lemb | Polinomios de Appell | spa |
| dc.subject.lemb | Sequences (Mathematics) | spa |
| dc.subject.lemb | Polynomials | spa |
| dc.subject.lemb | Appell polynomials | spa |
| dc.publisher.program | Maestría en Matemáticas Aplicadas | spa |
| dc.publisher.department | Escuela de Ciencias Exactas e Ingeniería | spa |
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| dc.type.coar | http://purl.org/coar/resource_type/c_bdcc | eng |
| dc.type.local | Tesis/Trabajo de grado - Monografía - Maestría | spa |
| dc.description.degreename | Magister en Matemáticas Aplicadas | spa |
| dc.description.degreelevel | Maestría | spa |
