Hyperbolic Sine and Cosine Integral Calculator (Shi, Chi)

Enter x to compute the hyperbolic sine integral Shi(x) and hyperbolic cosine integral Chi(x) via power series, with a curve plot.

Input

Enter a value of x to compute the hyperbolic sine integral Shi(x) and hyperbolic cosine integral Chi(x) using power series.

Value of x

Enter a real number (e.g. 1). Chi diverges at x=0.

Shi(1)

1.0572508754

Chi(1)

0.837866941

Input x

Curve of Shi(x)

The hyperbolic sine integral is defined as Shi(x)=∫_0^x sinh(t)/t dt and is an odd function.
The hyperbolic cosine integral is defined as Chi(x)=γ+ln|x|+∫_0^x (cosh(t)−1)/t dt, where γ is the Euler-Mascheroni constant.
Computation uses the power series Shi(x)=Σ x^(2n+1)/((2n+1)(2n+1)!) and the matching series for Chi.
At x=0, Shi(0)=0 while Chi(x) diverges to negative infinity as x approaches 0.
For very large |x| the terms grow rapidly, so a moderate range is practical in double precision.

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