Difference between revisions of "Scorer Gi"

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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
 
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
$$\mathrm{Gi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \sin \left( \dfrac{t^3}{3}+xt \right)dt.$$
+
$$\mathrm{Gi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \sin \left( \dfrac{t^3}{3}+xt \right) \mathrm{d}t.$$
  
 
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<gallery>
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File:Scorergiplot.png|Graph of $\mathrm{Gi}$.
 
File:Complexscorergi.png|[[Domain coloring]] of $\mathrm{Gi}$.
 
File:Complexscorergi.png|[[Domain coloring]] of $\mathrm{Gi}$.
 
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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