Difference between revisions of "Airy Ai"

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(Properties)
(References)
 
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[[Category:SpecialFunction]]
 
The Airy function $\mathrm{Ai}$ is a solution of the [[Airy differential equation]] linearly independent from the [[Airy Bi]] function.
 
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:Airyai.png|Airy $\mathrm{Ai}$ function.
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File:Airyaiplot.png|Graph of the Airy $\mathrm{Ai}$ function.
File:Complexairyai.png|[[Domain coloring]] of analytic continuation of $\mathrm{Ai}$.
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File:Complexairyaiplot.png|[[Domain coloring]] of Airy $\mathrm{Ai}$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
  
 
=Properties=
 
=Properties=
{{:Integral representation of Airy Ai}}
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[[Integral representation of Airy Ai]]<br />
{{:Value of Ai(0)}}
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[[Value of Ai(0)]]<br />
{{:Value of Ai'(0)}}
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[[Value of Ai'(0)]]<br />
{{:Relationship between Airy Ai and modified Bessel K}}
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[[Relationship between Airy Ai and modified Bessel K]]<br />
{{:Relationship between Scorer Gi and Airy functions}}
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[[Relationship between Scorer Gi and Airy functions]]<br />
{{:Relationship between Scorer Hi and Airy functions}}
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[[Relationship between Scorer Hi and Airy functions]]<br />
  
 
=Videos=
 
=Videos=
[https://www.youtube.com/watch?v=oYJq3mhg5yE&noredirect=1 Airy differential equation]<br />
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[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]<br />
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[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=HlX62TkR6gc&noredirect=1 Leading Tsunami wave reaching the shore]<br />
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[https://www.youtube.com/watch?v=oYJq3mhg5yE&noredirect=1 Airy differential equation (26 November 2013)]<br />
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=References=
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[http://www.ams.org/samplings/feature-column/fcarc-rainbows The mathematics of rainbows]<br />
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[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 />
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[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=
 
=See Also=
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[[Scorer Gi]] <br />
 
[[Scorer Gi]] <br />
 
[[Scorer Hi]] <br />
 
[[Scorer Hi]] <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 />
 
[http://www.people.fas.harvard.edu/~sfinch/csolve/ai.pdf Airy function zeros]
 

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.

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

See Also

Airy Bi
Scorer Gi
Scorer Hi