含幂函数、有理分式与三角函数的无穷积分——一个引理及其应用

Infinite integrals involving powers,rational functions and trigonometric functions——a lemma and its application

介绍了新近建立的一个引理.该引理给出幂函数与指数函数之积沿大圆弧的积分.利用该引理和留数定理导出了含幂函数、有理分式与三角函数的无穷积分的一般公式,结果用留数和有理分式的洛朗系数表出.计算了若干实例.

An introduction to a recently established lemma is presented. The lemma enables us to evaluate integrals involving powers and exponentials on a large semicircle. Based on the lemma and the residue theorem, two general for- mulae are derived for infinite integrals are expressed in terms of residues and involving powers, rational functions and trigonometric functions, and the results Laurent coefficients of the rational function. Several examples are given.