The Chi function, also called the hyperbolic cosine integral, is defined for complex numbers 
off the nonpositive real
axis by
 |
(1)
|
where 
is the Euler-Mascheroni
constant and 
uses the principal branch of the natural
logarithm (NIST DLMF, §6.2(ii)). The function is given by the Wolfram
Language command CoshIntegral[z].
The Chi function has a unique positive real root at 
(OEIS A133746).
The derivative of 
is
 |
(2)
|
and the integral is
 |
(3)
|
See also
Cosine Integral,
Shi,
Sine Integral
Related Wolfram sites
https://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.NIST Digital Library of Mathematical
Functions. "Definitions and Interrelations." §6.2(ii). https://dlmf.nist.gov/6.2.ii.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 Resource. https://mathworld.wolfram.com/Chi.html
Subject classifications
