라마누잔의 정적분

이 항목의 스프링노트 원문주소

• 라마누잔의 정적분

 

 

개요

Integrate[(x Exp[-x Sqrt[5]])/Cosh[x], {x, 0, \[Infinity]}] //  FullSimplify

http://www.wolframalpha.com/input/?i=Integrate[(x+Exp[-x+Sqrt[5]])/Cosh[x],+{x,+0,+[Infinity]}]+

http://www.wolframalpha.com/input/?i=(polygamma[1,(1%2Bsqrt(5))/4]-polygamma[1,(3%2Bsqrt(5))/4])/8

 

Integrate[(x^2 Exp[-x Sqrt[3]])/Sinh[x], {x, 0, \[Infinity]}] //FullSimplify

http://www.wolframalpha.com/input/?i=integrate[(x^2+Exp[-x+Sqrt[3]])/Sinh[x],+{x,+0,+Infinity}]

http://www.wolframalpha.com/input/?i=-polygamma[2,(1%2Bsqrt(3))/2]/4

 

 

Berndt, B. C. and Rankin, R. A. Ramanujan: Letters and Commentary. Providence, RI: Amer. Math. Soc., 1995.

 

 

재미있는 사실

•  

• Math Overflow

  • Ramanujan’s eccentric Integral formula
  • 연분수 http://mathoverflow.net/questions/49866/applications-of-finite-continued-fractions/

 

 

역사

 

• http://www.google.com/search?hl=en&tbs=tl:1&q=
• 수학사연표
•  

 

 

메모

 

 

관련된 항목들

• 트리감마 함수(trigamma function)

 

 

수학용어번역

• 단어사전 http://www.google.com/dictionary?langpair=en|ko&q=
• 발음사전 http://www.forvo.com/search/

• 대한수학회 수학 학술 용어집

  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 남·북한수학용어비교
• 대한수학회 수학용어한글화 게시판

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• http://mathworld.wolfram.com/RamanujanContinuedFractions.html
• http://www.wolframalpha.com/input/?i=
• NIST Digital Library of Mathematical Functions

• The On-Line Encyclopedia of Integer Sequences

  • http://www.research.att.com/~njas/sequences/?q=

 

 

관련논문

• http://www.jstor.org/action/doBasicSearch?Query=
• http://www.ams.org/mathscinet
• http://dx.doi.org/

 

 

관련도서

• 도서내검색

  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=

• 도서검색

  • http://books.google.com/books?q=
  • http://book.daum.net/search/mainSearch.do?query=
  • http://book.daum.net/search/mainSearch.do?query=

 

 

관련기사

• 네이버 뉴스 검색 (키워드 수정)

  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=

 

 

블로그

• 구글 블로그 검색

  • http://blogsearch.google.com/blogsearch?q=
• 네이버 오늘의과학
• Mathematical Moments from the AMS
• BetterExplained