Chi

$\begin{figure}\begin{center}\BoxedEPSF{Chi.epsf scaled 850}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{ChiReIm.epsf scaled 700}\end{center}\end{figure}$

$\begin{displaymath} \mathop{\rm Chi}(z)=\gamma+\ln z+\int_0^z {\cosh t-1\over t}\,dt, \end{displaymath}$

where $\gamma$ is the Euler-Mascheroni Constant. The function is given by the Mathematica ${}^{\scriptstyle\circledRsymbol}$ (Wolfram Research, Champaign, IL) command CoshIntegral[z].

See also Cosine Integral, Shi, Sine Integral

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Sine and Cosine Integrals.'' §5.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 231-233, 1972.