雅可比变换理论的来源初探  

A Preliminary Probe into the Origin of Jacobi's Transformation Theory

作　　者：徐快 李威[1] XU Kuai;LI Wei(Institute for Advanced Study in History of Science,Northwest University,Xi′an 710127,China)

机构地区：[1]西北大学科学史高等研究院,陕西西安710127

出　　处：《广西民族大学学报（自然科学版）》2023年第1期40-45,共6页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：国家自然科学基金项目(11901444);陕西省自然科学基础研究计划项目(2019JQ-870);中国博士后科学基金项目(2018M643716)。

摘　　要：雅可比的变换理论是19世纪椭圆函数论的关键内容,它的起源和发展更是数学史上至关重要的一部分。从18世纪的椭圆积分出发,详细分析勒让德的著作《积分练习》和雅可比在1827年的两篇文章中的变换思想,探寻雅克比变换理论的背景和来源。将相关数学家的变换方法进行研究并剖析其形成的动因,可以更深刻地理解雅可比的变换理论及其发展,进而对椭圆函数的早期历史有一个全面的了解。Jacobi's transformation theory is the key of elliptic function theory in 19th century,and its origin and development is a very important part in the history of mathematics.This paper will start from elliptic integrals in the 18th century,analyze the transformation ideas in Legendre's Exercices de calcul intégral and Jacobi's two papers in 1827 in detail,and explore the background and source of Jacobi's Transformation Theory.We can deeply understand Jacobi's transformation theory and its development,and then have a comprehensive understanding of the early history of elliptic functions by studying the transformation methods of relevant mathematicians and analyzing their causes.

关 键 词：椭圆函数 变换理论 雅可比 勒让德 

分 类 号：N09[自然科学总论—科学技术哲学]