千篇一律 发表于 2025-3-23 10:46:50

Theta Functions imposing both conditions, ‘doubly periodic’ and ‘holomorphic’, is too restrictive. When the condition ‘holomorphic’ is replaced by ‘meromorphic’, the fruitful theory of elliptic functions is developed, as we saw. In this chapter we loosen the condition ‘doubly periodic’.

Middle-Ear 发表于 2025-3-23 14:29:48

http://reply.papertrans.cn/31/3078/307796/307796_12.png

特征 发表于 2025-3-23 21:53:11

http://reply.papertrans.cn/31/3078/307796/307796_13.png

Diverticulitis 发表于 2025-3-23 22:53:39

http://reply.papertrans.cn/31/3078/307796/307796_14.png

天空 发表于 2025-3-24 06:05:31

https://doi.org/10.1007/978-3-8274-2853-0It is natural to call the former an . integral, but why call the latter ‘elliptic’, even though the curve is not an ellipse? In fact, today the word ‘elliptic integral’ is a general term used in the following sense.

CORE 发表于 2025-3-24 08:10:14

Ein Spielzeug mit GruppenstrukturIn this chapter, we are going to see how elliptic integrals are applied in mathematics and physics. Good mathematical objects appear in many situations.

enumaerate 发表于 2025-3-24 12:38:53

http://reply.papertrans.cn/31/3078/307796/307796_17.png

synovium 发表于 2025-3-24 15:35:59

Brennstoffe und ihre technische Verwendung,In the previous chapter we defined Jacobi’s elliptic function sn as the inverse function of the incomplete elliptic integral of the first kind, introduced cn and dn and studied their properties. These Jacobi’s elliptic functions appear in various problems, from which we pick up two applications to physics in this chapter.

dry-eye 发表于 2025-3-24 19:23:00

http://reply.papertrans.cn/31/3078/307796/307796_19.png

Crayon 发表于 2025-3-25 02:20:44

http://reply.papertrans.cn/31/3078/307796/307796_20.png
页: 1 [2] 3 4 5 6
查看完整版本: Titlebook: Elliptic Integrals and Elliptic Functions; Takashi Takebe Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusive l