Evaluate the integral ∫(-∞~∞) cos(tx)/(x²+1)^n dx,
where n is positive integer.
Integral
2011-08-28 9:58 am
回答 (4)
2011-09-10 6:00 pm
✔ 最佳答案
http://www.wolframalpha.com/input/?_=1315220945980&i=integrate+costx%2f(x%5e2%2b1)%5en%2cx%2c-inf%2cinf&fp=1&incTime=true2011-09-10 10:00:49 補充：
圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/improperintegral/difficultimproperintegral9.jpg
參考資料：
my wisdom of maths + formula from http://eqworld.ipmnet.ru/en/auxiliary/inttrans/FourCos2.pdf + http://eqworld.ipmnet.ru/en/auxiliary/inttrans/FourSin2.pdf
2011-09-11 7:33 pm
I thought you do not want an answer in the form of a summation. Otherwise the answer can be readily obtained by contour integration, right?
2011-09-11 7:17 am
請doraemonpaul證明一下, consider " ... ", OK!?
2011-09-10 23:17:41 補充：
團長證明您的答案,好嗎?
2011-09-10 23:17:41 補充：
團長證明您的答案,好嗎?
2011-09-11 3:16 am
Ans.
{∑(k=0~n-1) [t^(n-1-k)H(n,k)]/[2^k (n-1-k)!] }* π/[2^(n-1)e^t], n=1,2,3,...
{∑(k=0~n-1) [t^(n-1-k)H(n,k)]/[2^k (n-1-k)!] }* π/[2^(n-1)e^t], n=1,2,3,...
收錄日期: 2021-04-23 23:25:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110828000051KK00101