EVALUATION OF THE NON-ELEMENTARY INTEGRAL \(\int e^{\lambda x^\alpha}dx\), \(\alpha\ge 2\), AND OTHER RELATED INTEGRALS

EVALUATION OF THE NON-ELEMENTARY INTEGRAL \(\int e^{\lambda x^\alpha}dx\), \(\alpha\ge 2\), AND OTHER RELATED INTEGRALS

A formula for the non-elementary integral \(\int e^{\lambda x^\alpha} dx\) where \(\alpha\) is real and greater or equal two, is obtained in terms of the confluent hypergeometric function \(_{1}F_1\) by expanding the integrand as a Taylor series. This result is verified by directly evaluating the ar...

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Bibliographic Details
Main Author: Victor Nijimbere
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2017-12-01
Series:Ural Mathematical Journal
Subjects:
Non-elementary integral, Hypergeometric function, Confluent hypergeometric function, Asymptotic evaluation, Fundamental theorem of calculus, Gaussian, Maxwell-Bortsman distribution
Online Access:https://umjuran.ru/index.php/umj/article/view/91
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