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Chi


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The hyperbolic cosine integral, often called the "Chi function" for short, is defined by

 Chi(z)=gamma+lnz+int_0^z(cosht-1)/tdt,
(1)

where gamma is the Euler-Mascheroni constant. The function is given by the Wolfram Language command CoshIntegral[z].

The Chi function has a unique real root at x=0.52382257138... (OEIS A133746).

The derivative of Chi(z) is

 d/(dz)Chi(z)=(coshz)/z,
(2)

and the integral is

 intChi(z)dz=zChi(z)-sinhz.
(3)

See also

Cosine Integral, Shi, Sine Integral

Related Wolfram sites

http://functions.wolfram.com/GammaBetaErf/CoshIntegral/

Explore with Wolfram|Alpha

References

Abramowitz, M. and Stegun, I. 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.Sloane, N. J. A. Sequence A133746 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Chi

Cite this as:

Weisstein, Eric W. "Chi." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Chi.html

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