  RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Ural Math. J.: Year: Volume: Issue: Page: Find

 Personal entry: Login: Password: Save password Enter Forgotten password? Register

 Ural Math. J., 2018, Volume 4, Issue 1, Pages 43–55 (Mi umj54)  Evaluation of some non-elementary integrals involving sine, cosine, exponential and logarithmic integrals: part II

Victor Nijimbere

School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada

Abstract: The non-elementary integrals ${Si}_{\beta,\alpha}=\int [\sin{(\lambda x^\beta)}/(\lambda x^\alpha)] dx,$ $\beta\ge1,$ $\alpha>\beta+1$ and ${Ci}_{\beta,\alpha}=\int [\cos{(\lambda x^\beta)}/(\lambda x^\alpha)] dx,$ $\beta\ge1,$ $\alpha>2\beta+1$, where $\{\beta,\alpha\}\in\mathbb{R}$, are evaluated in terms of the hypergeometric function $_{2}F_3$. On the other hand, the exponential integral ${Ei}_{\beta,\alpha}=\int (e^{\lambda x^\beta}/x^\alpha) dx,$ $\beta\ge1,$ $\alpha>\beta+1$ is expressed in terms of $_{2}F_2$. The method used to evaluate these integrals consists of expanding the integrand as a Taylor series and integrating the series term by term.

Keywords: Non-elementary integrals, Sine integral, Cosine integral, Exponential integral, Logarithmic integral, Hyperbolic sine integral, Hyperbolic cosine integral, Hypergeometric functions.

DOI: https://doi.org/10.15826/umj.2018.1.004  Full text: PDF file (156 kB) Full text: https:/.../109 References: PDF file   HTML file

Bibliographic databases:  Language:

Citation: Victor Nijimbere, “Evaluation of some non-elementary integrals involving sine, cosine, exponential and logarithmic integrals: part II”, Ural Math. J., 4:1 (2018), 43–55 Citation in format AMSBIB
\Bibitem{Nij18} \by Victor~Nijimbere \paper Evaluation of some non-elementary integrals involving sine, cosine, exponential and logarithmic integrals: part II \jour Ural Math. J. \yr 2018 \vol 4 \issue 1 \pages 43--55 \mathnet{http://mi.mathnet.ru/umj54} \crossref{https://doi.org/10.15826/umj.2018.1.004} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR3848663} \elib{http://elibrary.ru/item.asp?id=35339281} 

• http://mi.mathnet.ru/eng/umj54
• http://mi.mathnet.ru/eng/umj/v4/i1/p43

 SHARE:      Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
Cycle of papers
•  Contact us: math-net2020_10 [at] mi-ras ru Terms of Use Registration Logotypes © Steklov Mathematical Institute RAS, 2020