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 (Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics, Henan Polytechnoc University) ;
  • Luo, Qiu-Ming (Department of Mathematcis, Jiaozuo University) ;
  • Guo, Bai-Ni (Department of Applied Mathematics, and Informatics, Research Institute of Applied Mathematics, Henan Polytechnic University)
  • 발행 : 2004.08.01

초록

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.