Difference between revisions of "Scorer Hi"

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The Scorer $\mathrm{Hi}$ 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 $\mathrm{Hi}$ function is a solution of the [[differential equation]] $y''(x)-x y(x)=\dfrac{1}{\pi}$ and may be defined by the formula
$$\mathrm{Hi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \exp \left( -\dfrac{t^3}{3}+xt \right)dt.$$
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$$\mathrm{Hi}(x)=\dfrac{1}{\pi} \displaystyle\int_0^{\infty} \exp \left( -\dfrac{t^3}{3}+xt \right)\mathrm{d}t.$$
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<div align="center">
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<gallery>
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File:Complexscorerhi.png|[[Domain coloring]] of $\mathrm{Hi}$.
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</gallery>
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</div>
  
 
=Properties=
 
=Properties=

Revision as of 22:46, 9 June 2016

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

Properties

Relationship between Scorer Hi and Airy functions

See Also

Airy Ai
Airy Bi
Scorer Gi