Gaussian integral by Taylor series and applications

• Autor(a) principal: Sales, Lázaro Lima de
• Data de Publicação: 2021
• Outros Autores: Silva, Jonatas Arizilanio, Souza, Eliângela Paulino Bento de, Souza, Hidalyn Theodory Clemente Mattos de, Farias, Antonio Diego Silva, Lavor, Otávio Paulino
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Remat (Bento Gonçalves)
• Texto Completo: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4330
• topic: Gaussian Integral; Special Functions; Fractional Derivative; Integral Gaussiana; Funções Especiais; Derivada Fracionária

In this paper, we present a solution for a specific Gaussian integral. Introducing a parameter that depends on a n index, we found out a general solution inspired by the Taylor series of a simple function. We demonstrated that this parameter represents the expansion coefficients of this function, a very interesting and new result. We also introduced some Theorems that are proved by mathematical induction. As a test for the solution presented here, we investigated a non-extensive version for the particle number density in Tsallis framework, which enabled us to evaluate the functionality of the method. Besides, solutions for a certain class of the gamma and factorial functions are derived. Moreover, we presented a simple application in fractional calculus. In conclusion, we believe in the relevance of this work because it presents a solution for the Gaussian integral from an unprecedented perspective.