Gaussian integral by Taylor series and applications

Lázaro Lima de Sales; Jonatas Arizilanio Silva; Eliângela Paulino Bento de Souza; Hidalyn Theodory Clemente Mattos de Souza; Antonio Diego Silva Farias; Otávio Paulino Lavor

doi:10.35819/remat2021v7i2id4330

Autores/as

Lázaro Lima de Sales Universidade do Estado do Rio Grande do Norte (UERN), Departamento de Física, Mossoró, RN, Brasil https://orcid.org/0000-0002-5352-6642
Jonatas Arizilanio Silva Universidade Federal Rural do Semi-Árido (UFERSA), Departamento de Ciência e Tecnologia (DCT), Caraúbas, RN, Brasil https://orcid.org/0000-0003-2246-1660
Eliângela Paulino Bento de Souza Universidade Federal da Paraíba (UFPB), Departamento de Física, João Pessoa, PB, Brasil https://orcid.org/0000-0002-4466-2802
Hidalyn Theodory Clemente Mattos de Souza Universidade Federal Rural do Semi-Árido (UFERSA), Departamento de Ciências Exatas e Naturais (DECEN), Pau dos Ferros, RN, Brasil https://orcid.org/0000-0002-7874-8188
Antonio Diego Silva Farias Universidade Federal Rural do Semi-Árido (UFERSA), Departamento de Ciências Exatas e Naturais (DECEN), Pau dos Ferros, RN, Brasil https://orcid.org/0000-0002-1222-7013
Otávio Paulino Lavor Universidade Federal Rural do Semi-Árido (UFERSA), Departamento de Ciências Exatas e Naturais (DECEN), Pau dos Ferros, RN, Brasil http://orcid.org/0000-0001-5237-3392

DOI:

https://doi.org/10.35819/remat2021v7i2id4330

Palabras clave:

Gaussian Integral, Special Functions, Fractional Derivative

Resumen

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.

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Biografía del autor/a

Lázaro Lima de Sales, Universidade do Estado do Rio Grande do Norte (UERN), Departamento de Física, Mossoró, RN, Brasil

http://lattes.cnpq.br/7727890574597438
Jonatas Arizilanio Silva, Universidade Federal Rural do Semi-Árido (UFERSA), Departamento de Ciência e Tecnologia (DCT), Caraúbas, RN, Brasil

http://lattes.cnpq.br/0385112916465731
Eliângela Paulino Bento de Souza, Universidade Federal da Paraíba (UFPB), Departamento de Física, João Pessoa, PB, Brasil

http://lattes.cnpq.br/5621970048397580
Hidalyn Theodory Clemente Mattos de Souza, Universidade Federal Rural do Semi-Árido (UFERSA), Departamento de Ciências Exatas e Naturais (DECEN), Pau dos Ferros, RN, Brasil

http://lattes.cnpq.br/1340176705421593
Antonio Diego Silva Farias, Universidade Federal Rural do Semi-Árido (UFERSA), Departamento de Ciências Exatas e Naturais (DECEN), Pau dos Ferros, RN, Brasil

http://lattes.cnpq.br/4450585340269458
Otávio Paulino Lavor, Universidade Federal Rural do Semi-Árido (UFERSA), Departamento de Ciências Exatas e Naturais (DECEN), Pau dos Ferros, RN, Brasil

http://lattes.cnpq.br/1857806253382088

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