Analytic and arithmetic methods in Liouville's identities

IF 0.5 3区 哲学 Q3 HISTORY & PHILOSOPHY OF SCIENCE
Maria Rosaria Enea , Giovanni Ferraro
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引用次数: 0

Abstract

The history of Liouville's identities is of remarkable interest especially as far as the methods used to prove them are concerned. In Liouville's opinion, the identities had to be proved by merely arithmetic considerations. Some mathematicians, such as Uspensky, developed Liouville's approach and used elementary methods. However, other mathematicians (among them Nazimoff and Bell) followed Hermite's suggestions of deriving Liouville's identities from the theory of elliptic functions: most of them thought that analytic methods were preferable since they allowed one to discover new identities (and not only to prove known ones).

刘维尔恒等式的解析和算术方法
刘维尔身份的历史是非常有趣的,特别是就用来证明他们的方法而言。在刘维尔看来,恒等式只能用算术方法来证明。一些数学家,如乌斯宾斯基,发展了刘维尔的方法,并使用了初等方法。然而,其他数学家(包括纳齐莫夫和贝尔)遵循了埃尔米特的建议,从椭圆函数理论中推导出刘维尔恒等式:他们中的大多数人认为解析方法更可取,因为它们允许人们发现新的恒等式(而不仅仅是证明已知的恒等式)。
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来源期刊
Historia Mathematica
Historia Mathematica 数学-科学史与科学哲学
CiteScore
1.10
自引率
0.00%
发文量
29
审稿时长
72 days
期刊介绍: Historia Mathematica publishes historical scholarship on mathematics and its development in all cultures and time periods. In particular, the journal encourages informed studies on mathematicians and their work in historical context, on the histories of institutions and organizations supportive of the mathematical endeavor, on historiographical topics in the history of mathematics, and on the interrelations between mathematical ideas, science, and the broader culture.
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