Difference between revisions of "Shi"

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The hyperbolic sine integral is defined by the formula
 
The hyperbolic sine integral is defined by the formula
$$\mathrm{Shi}(z)=\displaystyle\int_0^z \dfrac{\mathrm{sinh}(t)}{t} dt.$$
+
$$\mathrm{Shi}(z)=\displaystyle\int_0^z \dfrac{\mathrm{sinh}(t)}{t} \mathrm{d}t.$$
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Plot of hyperbolic sinh integral.png|Plot of $\mathrm{Shi}$ on $[-10,10]$.  
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File:Shiplot.png|Plot of $\mathrm{Shi}$.  
File:Domain coloring hyperbolic sine integral.png|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{Shi}$.
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File:Complexshiplot.png|[[Domain coloring]] of $\mathrm{Shi}$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
  
<center>{{:*-integral functions footer}}</center>
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{{:*-integral functions footer}}
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[[Category:SpecialFunction]]

Latest revision as of 23:11, 11 June 2016

The hyperbolic sine integral is defined by the formula $$\mathrm{Shi}(z)=\displaystyle\int_0^z \dfrac{\mathrm{sinh}(t)}{t} \mathrm{d}t.$$

$\ast$-integral functions