# 双曲函数

```双曲函数

，這裡的 是射線、雙曲線和x軸圍

、

sinh cosh tanh

,
）的直线之间

，垂線是
。

，則

）轉換正負號，就可得到相
[5]

（罗朗级数）

（罗朗

1. Weisstein, Eric W. ( ). Hyperbolic Functions. at MathWorld--A Wolfram Web Resource.
（原始内容存档于
） （英语）
Wolfram Research, Inc. [2020-08-29].
2022-05-21
.
2. Eves, Howard, Foundations and Fundamental Concepts of Mathematics, Courier Dover
Publications: 59, 2012, ISBN 9780486132204, “We also owe to Lambert the first systematic
development of the theory of hyperbolic functions and, indeed, our present notation for these
functions.”
3. Ratcliffe, John, Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics 149,
Springer: 99, 2006 [2014-03-27], ISBN 9780387331973,
2014-01-12 ,
“That the area of a hyperbolic triangle is proportional to its angle defect first appeared in
Lambert's monograph Theorie der Parallellinien, which was published posthumously in
1786.”
4. Augustus De Morgan (1849) Trigonometry and Double Algebra (http://books.google.com/boo
ks?id=7UwEAAAAQAAJ)
(https://web.archive.org/web/20140819012653/htt
（原始内容存档于
（页面存档备份
，存于互联网档案馆）
）
, Chapter VI: &quot;On
the connection of common and hyperbolic trigonometry&quot;
5. G. Osborn, Mnemonic for hyperbolic formulae (http://links.jstor.org/sici?sici=0025-5572(1902
07)2%3A2%3A34%3C189%3A1MFHF%3E2.0.CO%3B2-Z), The Mathematical Gazette, p.
189, volume 2, issue 34, July 1902

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