Shi

Min Max

Min   Max       Re       Im

The hyperbolic sine integral, often called the "Shi function" for short, is defined by

(1)

The function is implemented in the Wolfram Language as the function SinhIntegral[z].

It has Maclaurin series

			(2)
			(3)

(OEIS A061079).

It has derivative

(4)

and indefinite integral

(5)

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."