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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
Аннотация:
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.
Ключевые слова:
Non-elementary integrals, Sine integral, Cosine integral, Exponential integral, Logarithmic integral, Hyperbolic sine integral, Hyperbolic cosine integral, Hypergeometric functions.
Образец цитирования:
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
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/umj54 https://www.mathnet.ru/rus/umj/v4/i1/p43
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Страница аннотации: | 222 | PDF полного текста: | 53 | Список литературы: | 29 |
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