有关高阶奇异积分的Bertrand-Poincaré型换序公式

On Formulas of Bertrand-Poincaré Type Related to Singular Integrals of High Order

中文摘要:

      本文把关于Cauchy核奇异积分的Bertrand-Poincaré换序公式推广到高阶奇异积分的情况。主要结果见定理1至3,其中定理1已见于文献,但这里的表达方式和证法均是新的且较简。

英文摘要:

      In this note, the well-known Bertrand-Poincaré formula for changing order of integration related to singular intergrals with Cauchy kernel has been extended to some cases related to singular integrals of high order. The main results are Theorem 1 to Theorem 3, in which Theorem 1 had already been obtained in literature[5] but both its statement and its proof used here are new and simpler.