# 斯里尼瓦瑟·拉马努金

Srinivasa Ramanujan

英國

## 生平

### 在印度的成年阶段

${\displaystyle {\sqrt {\phi +2}}-\phi ={\cfrac {e^{-{\frac {2\pi }{5}}}}{1+{\cfrac {e^{-2\pi }}{1+{\cfrac {e^{-4\pi }}{1+{\cfrac {e^{-6\pi }}{1+\,\cdots }}}}}}}}=0.2840...}$

## 数学成就

${\displaystyle {\frac {1}{\pi }}={\frac {2{\sqrt {2}}}{9801}}\sum _{k=0}^{\infty }{\frac {(4k)!(1103+26390k)}{(k!)^{4}396^{4k}}}}$

${\displaystyle e^{\pi {\sqrt {58}}}=396^{4}-104.00000017...}$

${\displaystyle {\frac {1}{\left(1+2\sum _{n=1}^{\infty }{\frac {\cos n\theta }{\cosh n\pi }}\right)^{2}}}+{\frac {1}{\left(1+2\sum _{n=1}^{\infty }{\frac {\cosh n\theta }{\cosh n\pi }}\right)^{2}}}={\frac {2\Gamma ^{4}\left({\frac {3}{4}}\right)}{\pi }}}$

## 延伸閱讀

• Collected Papers of Srinivasa Ramanujan ISBN 0-8218-2076-1
• The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel ISBN 0-671-75061-5（中譯本：《知無涯者：拉馬努金傳》；羅伯特‧卡尼蓋爾著；胡樂士、齊民友譯；上海科技教育出版社；2002）

## 参考資料

• An overview of Ramanujan's notebooks by Bruce C. Berndt, in Charlemagne and His Heritage: 1200 Years of Civilization and Science in Europe， Volume 2: Mathematical Arts, P. L. Butzer, H. Th. Jongen, and W. Oberschelp, editors, Brepols, Turnhout, 1998, pp. 119-146，（22 pg. pdf file
• Modern Mathematicians， Harry Henderson, Facts on File Inc., 1996

## 外部链接

• The Ramanujan Journal
• 探求「無限」奧秘的數學家 一Srinivasa Ramanujan，顏一清，數學傳播季刊第27卷 第3,4期[1][2]