Shi
Shi
ShiReIm
ShiContours
The hyperbolic sine integral, often called the "Shi function" for short, is defined by
The function is implemented in the Wolfram Language as the function SinhIntegral [z].
It has Maclaurin series
Shi(z) = [画像:sum_(n=0)^(infty)(x^(2n+1))/((2n+1)^2(2n)!)]
(2)
= z+1/(18)z^3+1/(600)z^5+1/(35280)z^7+1/(326592)z^9+...
(3)
(OEIS A061079).
It has derivative
| [画像: (dShi(z))/(dz)=(sinhz)/z ] |
(4)
|
See also
Chi, Cosine Integral, Sine Integral, Sinhc FunctionRelated Wolfram sites
https://functions.wolfram.com/GammaBetaErf/SinhIntegral/Explore with Wolfram|Alpha
WolframAlpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). "Sine and Cosine Integrals." §5.2 inHandbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 231-233, 1972.Sloane, N. J. A. Sequence A061079 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
ShiCite this as:
Weisstein, Eric W. "Shi." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Shi.html