Difference between revisions of "Airy Ai"
(Created page with "The Airy function $\mathrm{Ai}$ is a solution of the Airy differential equation $$y''(z)-zy(z)=0.$$ <div align="center"> <gallery> File:Airyai.png|Airy $\mathrm{Ai}$ function....") |
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| − | The Airy function $\mathrm{Ai}$ is a solution of the Airy differential equation | + | __NOTOC__ |
| − | + | [[Category:SpecialFunction]] | |
| + | The Airy function $\mathrm{Ai}$ is a solution of the [[Airy differential equation]] linearly independent from the [[Airy Bi]] function. | ||
| + | |||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | File:Airyaiplot.png|Graph of the Airy $\mathrm{Ai}$ function. |
| − | File: | + | File:Complexairyaiplot.png|[[Domain coloring]] of Airy $\mathrm{Ai}$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
=Properties= | =Properties= | ||
| − | + | [[Integral representation of Airy Ai]]<br /> | |
| + | [[Value of Ai(0)]]<br /> | ||
| + | [[Value of Ai'(0)]]<br /> | ||
| + | [[Relationship between Airy Ai and modified Bessel K]]<br /> | ||
| + | [[Relationship between Scorer Gi and Airy functions]]<br /> | ||
| + | [[Relationship between Scorer Hi and Airy functions]]<br /> | ||
| + | |||
| + | =Videos= | ||
| + | [https://www.youtube.com/watch?v=HlX62TkR6gc&noredirect=1 Leading Tsunami wave reaching the shore (27 November 2009)]<br /> | ||
| + | [https://www.youtube.com/watch?v=0jnXdXfIbKk&noredirect=1 Series solution of ode: Airy's equation (3 November 2010)]<br /> | ||
| + | [https://www.youtube.com/watch?v=oYJq3mhg5yE&noredirect=1 Airy differential equation (26 November 2013)]<br /> | ||
| + | |||
| + | =References= | ||
| + | [http://www.ams.org/samplings/feature-column/fcarc-rainbows The mathematics of rainbows]<br /> | ||
| + | [http://www.ams.org/journals/mcom/1979-33-145/S0025-5718-1979-0514831-8/S0025-5718-1979-0514831-8.pdf Tables of Weyl Fractional Integrals for the Airy Function]<br /> | ||
| + | [http://www.amazon.com/Special-Functions-Introduction-Classical-Mathematical/dp/0471113131 Special Functions: An Introduction to the Classical Functions of Mathematical Physics]<br /> | ||
| + | |||
| + | =See Also= | ||
| + | [[Airy Bi]] <br /> | ||
| + | [[Scorer Gi]] <br /> | ||
| + | [[Scorer Hi]] <br /> | ||
Latest revision as of 02:00, 18 December 2016
The Airy function $\mathrm{Ai}$ is a solution of the Airy differential equation linearly independent from the Airy Bi function.
Graph of the Airy $\mathrm{Ai}$ function.
Domain coloring of Airy $\mathrm{Ai}$.
Properties
Integral representation of Airy Ai
Value of Ai(0)
Value of Ai'(0)
Relationship between Airy Ai and modified Bessel K
Relationship between Scorer Gi and Airy functions
Relationship between Scorer Hi and Airy functions
Videos
Leading Tsunami wave reaching the shore (27 November 2009)
Series solution of ode: Airy's equation (3 November 2010)
Airy differential equation (26 November 2013)
References
The mathematics of rainbows
Tables of Weyl Fractional Integrals for the Airy Function
Special Functions: An Introduction to the Classical Functions of Mathematical Physics
