<div style="text-align:justify;"> In this paper, we discuss the integrals of oscillatory kind function with Cauchy principal value in point zero which have the form like <img src="Edit_c0de6abb...<div style="text-align:justify;"> In this paper, we discuss the integrals of oscillatory kind function with Cauchy principal value in point zero which have the form like <img src="Edit_c0de6abb-c608-4dd4-98d0-a6138fad4d0a.png" width="70" height="40" alt="" />, where <em>f (x) </em>is smooth function and <em>r</em> is odd integer. In this integral, <em>x</em><sup><em>r </em></sup>has several stationary points <img src="Edit_da4ec557-4767-4f11-97ca-6be90a311d20.png" width="30" height="20" alt="" />, and the Cauchy principal value <img src="Edit_fcc0ee07-e3a9-4e31-8648-256af9b4f24a.png" width="50" height="30" alt="" />. We use some integral technique to transform it into the form like <img src="Edit_77d9cc9b-8a82-479a-be59-37e742db9672.png" width="70" height="40" alt="" /> so that we can calculate it. At the end, we give some numerical examples to prove the accuracy of this method. </div>展开更多
文摘<div style="text-align:justify;"> In this paper, we discuss the integrals of oscillatory kind function with Cauchy principal value in point zero which have the form like <img src="Edit_c0de6abb-c608-4dd4-98d0-a6138fad4d0a.png" width="70" height="40" alt="" />, where <em>f (x) </em>is smooth function and <em>r</em> is odd integer. In this integral, <em>x</em><sup><em>r </em></sup>has several stationary points <img src="Edit_da4ec557-4767-4f11-97ca-6be90a311d20.png" width="30" height="20" alt="" />, and the Cauchy principal value <img src="Edit_fcc0ee07-e3a9-4e31-8648-256af9b4f24a.png" width="50" height="30" alt="" />. We use some integral technique to transform it into the form like <img src="Edit_77d9cc9b-8a82-479a-be59-37e742db9672.png" width="70" height="40" alt="" /> so that we can calculate it. At the end, we give some numerical examples to prove the accuracy of this method. </div>
