Difference between revisions of "Chi"
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| − | The hyperbolic cosine integral $\mathrm{ | + | The hyperbolic cosine integral $\mathrm{Chi}$ is defined for $|\mathrm{arg}(z)| < \pi$ the formula |
| − | $$\mathrm{ | + | $$\mathrm{Chi}(z)=\gamma + \log(z) + \displaystyle\int_0^z \dfrac{\cosh(t)-1}{t} \mathrm{d}t,$$ |
| − | where $\gamma$ denotes the [[Euler-Mascheroni constant]], $\log$ denotes the [[logarithm]], and $\ | + | where $\gamma$ denotes the [[Euler-Mascheroni constant]], $\log$ denotes the [[logarithm]], and $\cosh$ denotes the [[cosh|hyperbolic cosine]]. |
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | File:Chiplot.png|Graph of $\mathrm{Chi}$. |
| + | File:Complexchiplot.png|[[Domain coloring]] of $\mathrm{Chi}$. | ||
</gallery> | </gallery> | ||
</div> | </div> | ||
| + | |||
| + | =Properties= | ||
| + | [[Derivative of chi]]<br /> | ||
| + | [[Antiderivative of chi]]<br /> | ||
| + | |||
| + | {{:*-integral functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 23:57, 10 December 2016
The hyperbolic cosine integral $\mathrm{Chi}$ is defined for $|\mathrm{arg}(z)| < \pi$ the formula $$\mathrm{Chi}(z)=\gamma + \log(z) + \displaystyle\int_0^z \dfrac{\cosh(t)-1}{t} \mathrm{d}t,$$ where $\gamma$ denotes the Euler-Mascheroni constant, $\log$ denotes the logarithm, and $\cosh$ denotes the hyperbolic cosine.
Graph of $\mathrm{Chi}$.
Domain coloring of $\mathrm{Chi}$.
Properties
Derivative of chi
Antiderivative of chi
