无穷乘积摘要 本文通过类比无穷级数，对无穷乘积的性质进行了研究和分析，给出类似于无穷级数的性质.通过类比无穷级数的审敛法，给出无穷乘积的审敛法，如比较判别法及其极限形式等.用棣莫弗公式与复变函数等知识将三角函数与双曲三角函数展开成无穷乘积的形式.但是无穷乘积又有其自身的特点.通过列举出常见的无穷乘积，从它的角度来解决部分极限与级数问题，即无穷乘积的应用.最后利用无穷乘积来探讨在考研过程中遇到的问题.关键词 无穷乘积 审敛法 性质 应用Infinite ProductAbstract In this paper, the properties of infinite product are studied and analyzed by analogy with infinite series, and the properties similar to infinite series are given. By comparing the convergence method of infinite series, in this paper, we give the convergence test of infinite product, such as the comparative test and its limit form, etc. Triangular function and hyperbolic trigonometric function are expanded into the form of infinite products by using the knowledge of De Moivre formula and complex variable function. However, infinite product has its own characteristics. By listing common infinite products, we can solve partial limit and series problems from the angle of infinite prducts, the application of infinite product, is solved from its angle. Finally, the problems encountered in the graduated entrance examination process are discussed by using infinite product.Key words infinite product criteria property application目 录引言....................................................................................11 无穷乘积收敛的定义与性质..............................................................41.1 无穷乘积的基本概念...........................................................41.2 无穷乘积的性质...............................................................52 无穷乘积的审敛法.....................................................................122.1 无穷乘积收敛性的一...
