• 제목/요약/키워드: $M_{\alpha}-integral$

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THE Mα-INTEGRAL

  • Park, Jae Myung;Ryu, Hyung Won;Lee, Hoe Kyoung
    • 충청수학회지
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    • 제23권1호
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    • pp.99-108
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    • 2010
  • In this paper, we define the $M_{\alpha}$-integral and investigate properties of the $M_{\alpha}$-integral.

THE n-DIMENSIONAL SPα AND Mα-INTEGRALS

  • Park, Jae-Myung
    • 충청수학회지
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    • 제15권2호
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    • pp.41-46
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    • 2003
  • In this paper, we investigate the $SP_{\alpha}$-integral and the $M_{\alpha}$-integral defined on an interval of the n-dimensional Euclidean space $\mathbb{R}^n$. In particular, we show that these two integrals are equivalent.

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EVALUATIONS OF THE IMPROPER INTEGRALS ${\int}_0^{\infty}$[sin$^{2m}({\alpha}x)]/(x^{2n})dx$ AND ${\int}_0^{\infty}$[sin$^{2m+1}({\alpha}x)]/(x^{2n+1})dx$

  • Qi, Feng;Luo, Qiu-Ming;Guo, Bai-Ni
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제11권3호
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    • pp.189-196
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    • 2004
  • In this article, using the L'Hospital rule, mathematical induction, the trigonometric power formulae and integration by parts, some integral formulae for the improper integrals ${\int}_0^{\infty}$[sin$^{2m}({\alpha}x)]/(x^{2n})dx$ AND ${\int}_0^{\infty}$[sin$^{2m+1}({\alpha}x)]/(x^{2n+1})dx$ are established, where m $\geq$ n are all positive integers and $\alpha$$\neq$ 0.

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