"라마누잔과 파이"의 두 판 사이의 차이

2009년 4월 2일 (목) 04:57 판

\(\frac{1}{\pi}= \frac{2\sqrt2}{9801}\sum_{n=0}^{\infty}\frac{(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}\)

\[\frac{426880 \sqrt{10005}}{\pi} = \sum_{k=0}^\infty \frac{(6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 (-640320)^{3k}}\!\]

Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
- J. M. Borwein, P. B. Borwein and D. H. Bailey
- The American Mathematical Monthly, Vol. 96, No. 3 (Mar., 1989), pp. 201-219
Modular equations and approximations to Pi
- S. Ramanujan
- Quart. J. Pure Appl. Math., (1914), vol. 45, p. 350-372
Approximations and complex multiplication according to Ramanujan
- D. V. Chudnovsky and G. V. Chudnovsky,
- Ramanujan Revisited, Academic Press Inc., Boston, (1988), p. 375-396 & p. 468-472.
A WZ Proof of Ramanujan's Formula for Pi
- Shalosh B. Ekhad and Doron Zeilberger
- `Geometry, Analysis, and Mechanics', ed. by J.M. Rassias, World Scientific, Singapore, 1994, 107-108.
Explicit Ramanujan-type approximations to pi of high order
- J. M. Borwein, P. B. Borwein
- 1987
Ramanujan's series for 1/π arising from his cubic and quartic theories of elliptic functions
- Nayandeep Deka Baruaha, and Bruce C. Berndt
- Journal of Mathematical Analysis and Applications, Volume 341, Issue 1, 2007
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@@ 51번째 줄: / 51번째 줄: @@
 <h5>관련된 고교수학 또는 대학수학</h5>
-* [[초기하급수(Hypergeometric series)|Hypergeometric functions]]
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 * [[산술기하평균함수(AGM)와 파이값의 계산|AGM과 파이값의 계산]]
 * [[타원적분(통합됨)|타원적분]]
-* [[#]]
+* [[모듈라 군, j-invariant and the singular moduli|The modular group, j-invariant and the singular moduli]]
+* [[초기하급수(Hypergeometric series)|Hypergeometric functions]]