Difference between revisions of "Scorer Gi"

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(Created page with "=See Also= Airy Ai<br /> Airy Bi<br /> Scorer Hi<br >")
 
 
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The Scorer $\mathrm{Gi}$ function is a solution of the [[differential equation]] $y''(x)-x y(x)=\dfrac{1}{\pi}$ and may be defined by the formula
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$$\mathrm{Gi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \sin \left( \dfrac{t^3}{3}+xt \right) \mathrm{d}t.$$
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<div align="center">
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<gallery>
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File:Scorergiplot.png|Graph of $\mathrm{Gi}$.
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File:Complexscorergi.png|[[Domain coloring]] of $\mathrm{Gi}$.
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</gallery>
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</div>
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=Properties=
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[[Relationship between Scorer Gi and Airy functions]]<br />
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=See Also=
 
=See Also=
 
[[Airy Ai]]<br />
 
[[Airy Ai]]<br />
 
[[Airy Bi]]<br />
 
[[Airy Bi]]<br />
 
[[Scorer Hi]]<br >
 
[[Scorer Hi]]<br >
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[[Category:SpecialFunction]]

Latest revision as of 23:03, 9 June 2016

The Scorer $\mathrm{Gi}$ function is a solution of the differential equation $y(x)-x y(x)=\dfrac{1}{\pi}$ and may be defined by the formula $$\mathrm{Gi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \sin \left( \dfrac{t^3}{3}+xt \right) \mathrm{d}t.$$

Properties

Relationship between Scorer Gi and Airy functions

See Also

Airy Ai
Airy Bi
Scorer Hi