"라마누잔(1887- 1920)"의 두 판 사이의 차이

2009년 12월 7일 (월) 22:00 판

라마누잔과 파이 항목에서 다룸
\(\frac{1}{\pi}= \frac{2\sqrt2}{9801}\sum_{n=0}^{\infty}\frac{(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}\)[[라마누잔과 파이|]]

nested radicals
\(\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+6\cdots}}}}} = 3\)

로저스-라마누잔 연분수와 항등식 항목에서 다룸
\(\cfrac{1}{1 + \cfrac{e^{-2\pi}}{1 + \cfrac{e^{-4\pi}}{1+\dots}}} = \left({\sqrt{5+\sqrt{5}\over 2}-{\sqrt{5}+1\over 2}}\right)e^{2\pi/5} = e^{2\pi/5}\left({\sqrt{\varphi\sqrt{5}}-\varphi}\right) = 0.9981360\dots\)

라마누잔이 하디에게 보낸 1913년의 편지에는 다음이 수록
\(k_{210}=\left(-1+\sqrt{2}\right)^2 \left(2-\sqrt{3}\right) \left(8-3 \sqrt{7}\right) \left(-\sqrt{6}+\sqrt{7}\right)^2 \left(-3+\sqrt{10}\right)^2 \left(4-\sqrt{15}\right)^2 \left(-\sqrt{14}+\sqrt{15}\right) \left(6-\sqrt{35}\right)\)

@@ 124번째 줄: / 124번째 줄: @@
 * [http://www.amazon.com/Ramanujans-Lost-Notebook-Part-Pt/dp/038725529X/ref=pd_sim_b_2 Ramanujan's Lost Notebook] : I, [http://www.amazon.com/Ramanujans-Lost-Notebook-Part-Pt/dp/0387777652/ref=pd_sim_b_3 II]<br>
 ** George E. Andrews and Bruce C. Berndt
+* Collected papers of Srinivasa Ramanujan, edited by G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson
 *  도서내검색<br>
 ** http://books.google.com/books?q=
@@ 133번째 줄: / 134번째 줄: @@
+.     .<1927><br>     Author: Ramanujan Aiyangar, Srinivasa, 1887-1920.<br> Published:<br> Location(s): Math QA37; .S7<br> Source: UCB Library Catalog<br>     2.     Ramanujan revisited : proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1-5, 1987 / edited by George E. Andrews ... [et al.].<1988><br>     Author: Ramanujan Centenary Conference (1987 : University of Illinois at Urbana-Champaign)<br> Published: Boston : Academic Press, c1988.
 <h5>관련논문</h5>