에어리 (Airy) 함수와 미분방정식

개요

• \(y'' - xy = 0\)

\(\mathrm{Ai}(x) = \frac{1}{\pi} \int_0^\infty \cos \left(\tfrac13t^3 + xt\right)\, dt,\)

\(\mathrm{Bi}(x) = \frac{1}{\pi} \int_0^\infty \left [\exp\left(-\tfrac13t^3 + xt\right) + \sin\left(\tfrac13t^3 + xt\right)\,\right]dt.,\)

http://www.wolframalpha.com/input/?i=Ai%28x%29

근사공식

• 안장점 근사
  \(x>>0\) 일 때,
  \( \mathrm{Ai}(x) \sim \frac{e^{-\frac{2 x^{3/2}}{3}}}{2 \sqrt{\pi } \sqrt[4]{x}}\)
  \(x<<0\) 일 때,
  \(\mathrm{Ai}(x) \sim \frac{\sin \left(\frac{2|x|^{3/2}}{3}+\frac{\pi }{4}\right)}{\sqrt{\pi } \sqrt[4]{|x|}}\)
  
• Asymptotics of the Airy Function
  

역사

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

메모

• Math Overflow http://mathoverflow.net/search?q=

수학용어번역

• 단어사전
  
  • http://www.google.com/dictionary?langpair=en%7Cko&q=
  • http://ko.wiktionary.org/wiki/
• 발음사전
  
  • http://www.forvo.com/word/airy/#en
  • 아이어리?
• [http://mathnet.kaist.ac.kr/mathnet/math_list.php?

mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]

• • http://mathnet.kaist.ac.kr/mathnet/math_list.php?

mode=list&ftype=eng_term&fstr=

• [http://www.nktech.net/science/term/term_l.jsp?

l_mode=cate&s_code_cd=MA 남·북한수학용어비교]

[http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?

bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A

%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE

%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학

용어한글화 게시판]

매스매티카 파일 및 계산 리소스

https://docs.google.com/file/d/0B8XXo8Tve1cxbl96STk2T3dpajg/

edit

• http://www.wolframalpha.com/input/?i=
• http://functions.wolfram.com/
• [http://dlmf.nist.gov/ NIST Digital Library of

Mathematical Functions]

• [http://people.math.sfu.ca/%7Ecbm/aands/toc.htm Abramowitz

and Stegun Handbook of mathematical functions]

• [http://www.research.att.com/%7Enjas/sequences/index.html

The On-Line Encyclopedia of Integer Sequences]

[http://numbers.computation.free.fr/Constants/constants.html

Numbers, constants and computation]

• [https://docs.google.com/open?

id=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIx

NmIw 매스매티카 파일 목록]

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Airy_equation
• http://en.wikipedia.org/wiki/WKB_approximation
• [http://eom.springer.de/default.htm The Online

Encyclopaedia of Mathematics]

• [http://dlmf.nist.gov/ NIST Digital Library of

Mathematical Functions]

• [http://eqworld.ipmnet.ru/ The World of Mathematical

Equations]

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=