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)

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