Lagrange Interpolation Formula and Arithmetic Progressions of Higher Order

Lagrange Interpolation Formula (LIF) has an important role in problems about unknown polynomials with known values in only some points. However this is not the only critic role of LIF. In this paper we shed light on some less known aspects of LIF. We use it to prove identities, and we show its relat...

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Main Authors:	Magalhaes, Cicero, Safaei, Navid
Format:	info:eu-repo/semantics/article
Language:	por
Published:	Universidad Antonio Nariño 2023
Subjects:	Interpolation, Lagrange, arithmetic progressionsp, mathematical competitions. Interpolação, Lagrange, progressões aritméticas, competições matemáticas
Online Access:	https://revistas.uan.edu.co/index.php/espaciomatematico/article/view/1480 https://repositorio.uan.edu.co/handle/123456789/11563
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author	Magalhaes, Cicero Safaei, Navid
author_facet	Magalhaes, Cicero Safaei, Navid
author_sort	Magalhaes, Cicero
collection	DSpace
description	Lagrange Interpolation Formula (LIF) has an important role in problems about unknown polynomials with known values in only some points. However this is not the only critic role of LIF. In this paper we shed light on some less known aspects of LIF. We use it to prove identities, and we show its relation with derivation and its applications to arithmetic progressions of higher order, introducing the finite dierences operator which opens a fan of possibilities for students preparing for mathematical competitions.
format	info:eu-repo/semantics/article
id	repositorio.uan.edu.co-123456789-11563
institution	Repositorio Digital UAN
language	por
publishDate	2023
publisher	Universidad Antonio Nariño
record_format	dspace
spelling	repositorio.uan.edu.co-123456789-115632024-10-11T20:03:47Z Lagrange Interpolation Formula and Arithmetic Progressions of Higher Order Fórmula da interpolación de Lagrange y progresiones aritméticas de orden superior Formula da interpolação de Lagrange e progressões aritméticas de ordem superior Magalhaes, Cicero Safaei, Navid Interpolation, Lagrange, arithmetic progressionsp, mathematical competitions. Interpolação, Lagrange, progressões aritméticas, competições matemáticas Lagrange Interpolation Formula (LIF) has an important role in problems about unknown polynomials with known values in only some points. However this is not the only critic role of LIF. In this paper we shed light on some less known aspects of LIF. We use it to prove identities, and we show its relation with derivation and its applications to arithmetic progressions of higher order, introducing the finite dierences operator which opens a fan of possibilities for students preparing for mathematical competitions. A Fórmula de Interpolação de Lagrange (FIL) tem um papel imenso em investigar problemas sobre polinômios desconhecidos com apenas valores conhecidos em alguns pontos. No entanto, este não é o único papel crítico da FIL. Neste artigo, lançamos mais luz sobre alguns aspectos menos conhecidos da FIL. Devemos adotá-la para provar identidades, sua relação com a derivação e, a fortiori, suas aplicações em progressões aritméticas de ordem superior, introduzindo o operador de diferenças finitas que, por si só, abrirá um novo leque para os competidores que estão se preparando para competições matemáticas. 2023-09-25 2024-10-11T20:03:47Z 2024-10-11T20:03:47Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artículo revisado por pares https://revistas.uan.edu.co/index.php/espaciomatematico/article/view/1480 10.54104/em.v2i1.1480 https://repositorio.uan.edu.co/handle/123456789/11563 por https://revistas.uan.edu.co/index.php/espaciomatematico/article/view/1480/1145 Derechos de autor 2022 ESPACIO MATEMÁTICO application/pdf Universidad Antonio Nariño ESPACIO MATEMÁTICO Journal; Vol. 2 No. 1 (2021); 58-67 Espacio Matemático; Vol. 2 Núm. 1 (2021); 58-67 ESPACIO MATEMÁTICO; Vol. 2 No 1 (2021); 58-67 Revista Espacio Matemático; v. 2 n. 1 (2021); 58-67 2711-1792 10.54104/em.v2i1
spellingShingle	Interpolation, Lagrange, arithmetic progressionsp, mathematical competitions. Interpolação, Lagrange, progressões aritméticas, competições matemáticas Magalhaes, Cicero Safaei, Navid Lagrange Interpolation Formula and Arithmetic Progressions of Higher Order
title	Lagrange Interpolation Formula and Arithmetic Progressions of Higher Order
title_full	Lagrange Interpolation Formula and Arithmetic Progressions of Higher Order
title_fullStr	Lagrange Interpolation Formula and Arithmetic Progressions of Higher Order
title_full_unstemmed	Lagrange Interpolation Formula and Arithmetic Progressions of Higher Order
title_short	Lagrange Interpolation Formula and Arithmetic Progressions of Higher Order
title_sort	lagrange interpolation formula and arithmetic progressions of higher order
topic	Interpolation, Lagrange, arithmetic progressionsp, mathematical competitions. Interpolação, Lagrange, progressões aritméticas, competições matemáticas
url	https://revistas.uan.edu.co/index.php/espaciomatematico/article/view/1480 https://repositorio.uan.edu.co/handle/123456789/11563
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