On a system of differential equations leading to periodic functions
On a system of differential equations leading to periodic functions
复制标题
关于导出周期函数的微分方程组
DOI：
10.1007/bf02421301
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发表时间：
1903
期刊：
影响因子：
3.7
通讯作者：
H. Baker
中科院分区：
文献类型：
--
作者：
H. Baker
本文包含了所有超椭圆σ函数所满足的微分方程组的初等代数推导，我们相信，这些函数是在《剑桥哲学会会刊》第九卷第九部分第1898页第513页中首次提出的，但没有说明。在该说明中将发现指示的方法的解决方案的方程与理论，认为皮卡尔，积分的全微分，和方法，从他们获得的任何扩展的sigma函数，和他们的使用，在情况p-2，表示几何的库默的十六节点四次曲面。直接从这些微分方程建立一个理论的sigma函数将出现可能是最大的cumestiveness的发展理论的函数的几个变量。正是从这个一般的观点来看，方程似乎本作家是特殊的兴趣;虽然他们的简单性也建议他们仅仅作为一个贡献的理论hyperUiptic职能。
The present paper contains an elementary algebraic deduction of a system of differential equations satisfied by all the hyperelliptic sigma functions which, as is believed, were first stated, but withou~ demonsh~ tion, in the Proceedings of the Cambridge Philosophical Society, Vol. IX, Part IX, I898, p. 513. In that note will be found indications of a method of solution of the equations in connexion with the theory, considered by PICARD, Of integrals of total differentials, and of a method of obtaining from them the expansion of any sigma function, and of their use, in case p-2, for expressing the geometry of KUMMER'S sixteen nodal quartic surface. The establishment of a theory of the sigma functions directly from these differential equations would appear likely to be of the greatest suggestiveness for the development of the theory of functions of several variables. It is from this general point of view that the equations appear to the present writer to be of peculiar interest; though their simplicity would also recommend them merely as a contribution to the theory of the hypereUiptic functions.