"에어리 (Airy) 함수와 미분방정식"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) (→근사공식) |
Pythagoras0 (토론 | 기여) 잔글 (Pythagoras0(토론)의 편집을 http://bomber0.myid.net/의 마지막 버전으로 되돌림) |
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| − | = | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 수학노트 원문주소</h5> |
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| − | + | <h5>개요</h5> | |
| − | <math> | + | * <math>y'' - xy = 0</math> |
| − | + | <math>\mathrm{Ai}(x) = \frac{1}{\pi} \int_0^\infty \cos\left(\tfrac13t^3 + xt\right)\, dt,</math> | |
| − | + xt\right)\,\right]dt.,</math> | + | <math>\mathrm{Bi}(x) = \frac{1}{\pi} \int_0^\infty \left[\exp\left(-\tfrac13t^3 + xt\right) + \sin\left(\tfrac13t^3 + xt\right)\,\right]dt.,</math> |
http://www.wolframalpha.com/input/?i=Ai%28x%29 | http://www.wolframalpha.com/input/?i=Ai%28x%29 | ||
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| − | + | <h5 style="margin: 0px; line-height: 2em;">근사공식</h5> | |
| − | + | * [[안장점 근사]]<br><math>x>>0</math> 일 때,<br><math>\mathrm{Ai}(x) \sim \frac{e^{-\frac{2 x^{3/2}}{3}}}{2 \sqrt{\pi } \sqrt[4]{x}}</math><br><math>x<<0</math> 일 때,<br><math>\mathrm{Ai}(x) \sim \frac{\sin \left(\frac{2 |x|^{3/2}}{3}+\frac{\pi }{4}\right)}{\sqrt{\pi } \sqrt[4]{|x|}}</math><br> | |
| + | * [http://www.math.umn.edu/%7Eymori/docs/teaching/fall08/airy.pdf Asymptotics of the Airy Function]<br> | ||
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| − | + | <h5>역사</h5> | |
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* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
* [[수학사연표 (역사)|수학사연표]] | * [[수학사연표 (역사)|수학사연표]] | ||
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| − | + | <h5>메모</h5> | |
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* Math Overflow http://mathoverflow.net/search?q= | * Math Overflow http://mathoverflow.net/search?q= | ||
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| − | + | <h5>관련된 항목들</h5> | |
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| − | = | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역</h5> |
* 단어사전<br> | * 단어사전<br> | ||
| 65번째 줄: | 69번째 줄: | ||
** http://www.forvo.com/word/airy/#en | ** http://www.forvo.com/word/airy/#en | ||
** 아이어리? | ** 아이어리? | ||
| − | * [http://mathnet.kaist.ac.kr/mathnet/math_list.php? | + | * [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br> |
| − | + | ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | |
| − | mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br> | + | * [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교] |
| − | ** http://mathnet.kaist.ac.kr/mathnet/math_list.php? | + | * [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 수학용어한글화 게시판] |
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| − | mode=list&ftype=eng_term&fstr= | ||
| − | * [http://www.nktech.net/science/term/term_l.jsp? | ||
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| − | l_mode=cate&s_code_cd=MA 남·북한수학용어비교] | ||
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| − | [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp? | ||
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| − | bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A | ||
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| − | %7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE | ||
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| − | + | <h5>매스매티카 파일 및 계산 리소스</h5> | |
| − | edit | + | * https://docs.google.com/file/d/0B8XXo8Tve1cxbl96STk2T3dpajg/edit |
* http://www.wolframalpha.com/input/?i= | * http://www.wolframalpha.com/input/?i= | ||
* http://functions.wolfram.com/ | * http://functions.wolfram.com/ | ||
| − | * [http://dlmf.nist.gov/ NIST Digital Library of | + | * [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=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIxNmIw 매스매티카 파일 목록] | ||
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| − | + | <h5>사전 형태의 자료</h5> | |
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* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* http://en.wikipedia.org/wiki/Airy_equation | * http://en.wikipedia.org/wiki/Airy_equation | ||
* http://en.wikipedia.org/wiki/WKB_approximation | * http://en.wikipedia.org/wiki/WKB_approximation | ||
| − | * [http://eom.springer.de/default.htm The Online | + | * [http://eom.springer.de/default.htm The Online Encyclopaedia of Mathematics] |
| − | + | * [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | |
| − | Encyclopaedia of Mathematics] | + | * [http://eqworld.ipmnet.ru/ The World of Mathematical Equations] |
| − | * [http://dlmf.nist.gov/ NIST Digital Library of | ||
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| − | Mathematical Functions] | ||
| − | * [http://eqworld.ipmnet.ru/ The World of Mathematical | ||
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| − | Equations] | ||
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| − | + | <h5>리뷰논문, 에세이, 강의노트</h5> | |
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| − | + | <h5>관련논문</h5> | |
* http://www.jstor.org/action/doBasicSearch?Query= | * http://www.jstor.org/action/doBasicSearch?Query= | ||
| 156번째 줄: | 120번째 줄: | ||
* http://dx.doi.org/ | * http://dx.doi.org/ | ||
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| − | + | <h5>관련도서</h5> | |
* 도서내검색<br> | * 도서내검색<br> | ||
** http://books.google.com/books?q= | ** http://books.google.com/books?q= | ||
** http://book.daum.net/search/contentSearch.do?query= | ** http://book.daum.net/search/contentSearch.do?query= | ||
2012년 10월 21일 (일) 14:08 판
이 항목의 수학노트 원문주소
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
메모
- Math Overflow http://mathoverflow.net/search?q=
관련된 항목들
수학용어번역
- 단어사전
- 발음사전
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
매스매티카 파일 및 계산 리소스
- https://docs.google.com/file/d/0B8XXo8Tve1cxbl96STk2T3dpajg/edit
- http://www.wolframalpha.com/input/?i=
- http://functions.wolfram.com/
- NIST Digital Library of Mathematical Functions
- Abramowitz and Stegun Handbook of mathematical functions
- The On-Line Encyclopedia of Integer Sequences
- Numbers, constants and computation
- 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
- The Online Encyclopaedia of Mathematics
- NIST Digital Library of Mathematical Functions
- The World of Mathematical Equations
리뷰논문, 에세이, 강의노트
관련논문