Difference between revisions of "Airy Bi"

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The Airy function $\mathrm{Bi}$ (sometimes called the "Bairy function") is a solution of the Airy differential equation
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__NOTOC__
$$y''(z)-zy(z)=0,$$
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which is linearly independent from the [[Airy Ai]] function.
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The Airy function $\mathrm{Bi}$ (sometimes called the "Bairy function") is a solution of the [[Airy differential equation]]
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$$y' '(z)-zy(z)=0,$$
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which is [[linearly independent]] from the [[Airy Ai]] function.
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Airybi.png|Aairy $\mathrm{Bi}$ function.
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File:Airybiplot.png|Aairy $\mathrm{Bi}$ function.
File:Complexairybi.png|[[Domain coloring]] of analytic continuation of $\mathrm{Bi}$.
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File:Complexairybiplot.png|[[Domain coloring]] of $\mathrm{Bi}$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
  
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=Properties=
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[[Relationship between Airy Bi and modified Bessel I]]<br />
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[[Relationship between Scorer Gi and Airy functions]]<br />
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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 />
  
 
=References=
 
=References=
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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 />
 
[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]
 
[http://www.people.fas.harvard.edu/~sfinch/csolve/ai.pdf Airy function zeros]
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=See Also=
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[[Airy Ai]] <br />
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[[Scorer Gi]] <br />
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[[Scorer Hi]] <br />
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[[Category:SpecialFunction]]

Latest revision as of 16:07, 21 October 2017


The Airy function $\mathrm{Bi}$ (sometimes called the "Bairy function") is a solution of the Airy differential equation $$y' '(z)-zy(z)=0,$$ which is linearly independent from the Airy Ai function.

Properties

Relationship between Airy Bi and modified Bessel I
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
Airy function zeros

See Also

Airy Ai
Scorer Gi
Scorer Hi