"오일러-맥클로린 공식"의 두 판 사이의 차이

2009년 4월 29일 (수) 04:12 판

\(\sum_{i=0}^n f(i) = \int^n_0f(x)\,dx-B_1(f(n)+f(0))+\sum_{k=2}^p\frac{B_k}{k!}\left(f^{(k-1)}(n)-f^{(k-1)}(0)\right)+R\)

\(\left|R\right|\leq\frac{2}{(2\pi)^{2(p+1)}}\int_0^n\left|f^{(p)}(x)\right|\,dx\)

\(B_0=1\), \(B_1=-{1 \over 2}\), \(B_2={1\over 6}\), \(B_3=0\), \(B_4=-\frac{1}{30}\), \(B_5=0\), \(B_6=\frac{1}{42}\)

@@ 8번째 줄: / 8번째 줄: @@
 <math>\left|R\right|\leq\frac{2}{(2\pi)^{2(p+1)}}\int_0^n\left|f^{(p)}(x)\right|\,dx</math>
+<math>B_0=1</math>, <math>B_1=-{1 \over 2}</math>, <math>B_2={1\over 6}</math>, <math>B_3=0</math>, <math>B_4=-\frac{1}{30}</math>, <math>B_5=0</math>, <math>B_6=\frac{1}{42}</math>
@@ 45번째 줄: / 47번째 줄: @@
 * [[스털링 공식]]
+* [[거듭제곱의 합을 구하는 공식]]
@@ 64번째 줄: / 67번째 줄: @@
 ** E. Hairer (Author), G. Wanner
 ** From [http://www.amazon.com/Analysis-History-Undergraduate-Mathematics-Readings/dp/0387945512 Analysis by Its History], 160-169p
-* Dances between continuous and discrete: Euler's summation formula
+* [http://www.math.nmsu.edu/%7Edavidp/euler2k2.pdf Dances between continuous and discrete: Euler's summation formula]<br>
-*
+** David J. Pengelley
-* in: Robert Bradley and Ed Sandifer (Eds), Proceedings, Euler 2K+2 Conference (Rumford, Maine, 2002) , Euler Society, 2003.
+** in: Robert Bradley and Ed Sandifer (Eds), Proceedings, Euler 2K+2 Conference (Rumford, Maine, 2002) , Euler Society, 2003.
 * [http://dx.doi.org/10.2307%2F2589145 An Elementary View of Euler's Summation Formula]<br>
 ** Tom M. Apostol