Difference between revisions of "Chi"
From specialfunctionswiki
| Line 5: | Line 5: | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File:Chiplot.png|Graph of $\mathrm{Chi} | + | File:Chiplot.png|Graph of $\mathrm{Chi}$. |
File:Complexchiplot.png|[[Domain coloring]] of $\mathrm{Chi}$. | File:Complexchiplot.png|[[Domain coloring]] of $\mathrm{Chi}$. | ||
</gallery> | </gallery> | ||
Revision as of 22:00, 23 May 2016
The hyperbolic cosine integral $\mathrm{Chi} \colon (0,\infty) \rightarrow \mathbb{R}$ is defined by the formula $$\mathrm{Chi}(z)=-\displaystyle\int_z^{\infty} \dfrac{\mathrm{cosh}(t)}{t} \mathrm{d}t=\gamma + \log(z) + \displaystyle\int_0^z \dfrac{\mathrm{cosh}(t)-1}{t} \mathrm{d}t,$$ where $\gamma$ denotes the Euler-Mascheroni constant, $\log$ denotes the logarithm, and $\mathrm{cosh}$ denotes the hyperbolic cosine function.
Graph of $\mathrm{Chi}$.
Domain coloring of $\mathrm{Chi}$.
