论文标题
包含参数的函数积分
Integrals of functions containing parameters
论文作者
论文摘要
本文最初提供了对当前计算无限积分实践的次要技术纠正，并介绍了“ Kahanian集成常数”的想法。但是，这种次要纠正的总影响可能很大，因为当前的实践是在大学阶段和许多学生中教授的 - 大多数学生并没有继续成为数学专业。此外，计算机代数系统已变得广泛，其中包括良好的免费系统，其中一些可用于智能手机。大多数当前的计算机代数系统应用当前的教科书规则，并扩大基本“次要”错误的影响，例如我们在本文中解决的连续性错误。因此，实际上，我们提出的更正很重要。
This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor correction is potentially large because the current practice is taught early at the university level and to very many students---most of whom do not go on to become mathematics majors. Moreover, computer algebra systems have become widespread, including good free ones, some of which are available for smartphones. Most current computer algebra systems apply current textbook rules and amplify the effects of fundamental "minor" errors such as the error in continuity that we address in this article. So in practice, the correction we present is important.
