"에어리 (Airy) 함수와 미분방정식"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
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| 9번째 줄: | 9번째 줄: | ||
http://www.wolframalpha.com/input/?i=Ai%28x%29 | http://www.wolframalpha.com/input/?i=Ai%28x%29 | ||
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==근사공식== | ==근사공식== | ||
| 44번째 줄: | 37번째 줄: | ||
* Math Overflow http://mathoverflow.net/search?q= | * Math Overflow http://mathoverflow.net/search?q= | ||
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| 54번째 줄: | 45번째 줄: | ||
==수학용어번역== | ==수학용어번역== | ||
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** http://ko.wiktionary.org/wiki/ | ** http://ko.wiktionary.org/wiki/ | ||
* 발음사전<br> | * 발음사전<br> | ||
** http://www.forvo.com/word/airy/#en | ** http://www.forvo.com/word/airy/#en | ||
** 아이어리? | ** 아이어리? | ||
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| 72번째 줄: | 55번째 줄: | ||
* https://docs.google.com/file/d/0B8XXo8Tve1cxbl96STk2T3dpajg/edit | * https://docs.google.com/file/d/0B8XXo8Tve1cxbl96STk2T3dpajg/edit | ||
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| 98번째 줄: | 72번째 줄: | ||
==리뷰논문, 에세이, 강의노트== | ==리뷰논문, 에세이, 강의노트== | ||
| + | * Duistermaat, J. J. “The Light in the Neighborhood of a Caustic.” In Séminaire Bourbaki Vol. 1976/77 Exposés 489–506, 19–29. Lecture Notes in Mathematics 677. Springer Berlin Heidelberg, 1978. http://link.springer.com/chapter/10.1007/BFb0070750. | ||
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| + | ==관련논문== | ||
| + | * Duistermaat, J. J. “Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities.” Communications on Pure and Applied Mathematics 27 (1974): 207–81. | ||
| + | * On the Intensity of Light in the Neighborhood of a Caustic, 1838. http://archive.org/details/cbarchive_36815_ontheintensityoflightintheneig1838. | ||
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[[분류:미분방정식]] | [[분류:미분방정식]] | ||
2015년 8월 19일 (수) 00:34 판
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
- 점근 급수(asymptotic series)
수학용어번역
매스매티카 파일 및 계산 리소스
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
- Duistermaat, J. J. “The Light in the Neighborhood of a Caustic.” In Séminaire Bourbaki Vol. 1976/77 Exposés 489–506, 19–29. Lecture Notes in Mathematics 677. Springer Berlin Heidelberg, 1978. http://link.springer.com/chapter/10.1007/BFb0070750.
관련논문
- Duistermaat, J. J. “Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities.” Communications on Pure and Applied Mathematics 27 (1974): 207–81.
- On the Intensity of Light in the Neighborhood of a Caustic, 1838. http://archive.org/details/cbarchive_36815_ontheintensityoflightintheneig1838.