Chi

Min Max

Min   Max       Re       Im

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

(1)

where  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  (OEIS A133746).

The derivative of  is

(2)

and the integral is

(3)

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."