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 | ||
| − | $$\mathrm{Gi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \sin \left( \dfrac{t^3}{3}+xt \right) | + | $$\mathrm{Gi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \sin \left( \dfrac{t^3}{3}+xt \right) \mathrm{d}t.$$ |
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| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Scorergiplot.png|Graph of $\mathrm{Gi}$. | ||
| + | File:Complexscorergi.png|[[Domain coloring]] of $\mathrm{Gi}$. | ||
| + | </gallery> | ||
| + | </div> | ||
=Properties= | =Properties= | ||
Latest revision as of 23:03, 9 June 2016
The Scorer $\mathrm{Gi}$ function is a solution of the differential equation $y(x)-x y(x)=\dfrac{1}{\pi}$ and may be defined by the formula $$\mathrm{Gi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \sin \left( \dfrac{t^3}{3}+xt \right) \mathrm{d}t.$$
Graph of $\mathrm{Gi}$.
Domain coloring of $\mathrm{Gi}$.
Properties
Relationship between Scorer Gi and Airy functions
