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).

中文翻译：

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刘维尔恒等式中的解析和算术方法

摘要 刘维尔恒等式的历史非常有趣，尤其是就用来证明它们的方法而言。在刘维尔看来，恒等式只能通过算术考虑来证明。一些数学家，例如 Uspensky，开发了 Liouville 的方法并使用了基本方法。然而，其他数学家（包括纳齐莫夫和贝尔）遵循 Hermite 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分析方法更可取，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） ）。