SciPy

scipy.special.shichi

scipy.special.shichi(x, out=None) = <ufunc 'shichi'>

Hyperbolic sine and cosine integrals.

The hyperbolic sine integral is

\[\int_0^x \frac{\sinh{t}}{t}dt\]

and the hyperbolic cosine integral is

\[\gamma + \log(x) + \int_0^x \frac{\cosh{t} - 1}{t} dt\]

where \(\gamma\) is Euler’s constant and \(\log\) is the principle branch of the logarithm.

Parameters:

x : array_like

Real or complex points at which to compute the hyperbolic sine and cosine integrals.

Returns:

si : ndarray

Hyperbolic sine integral at x

ci : ndarray

Hyperbolic cosine integral at x

Notes

For real arguments with x < 0, chi is the real part of the hyperbolic cosine integral. For such points chi(x) and chi(x + 0j) differ by a factor of 1j*pi.

For real arguments the function is computed by calling Cephes’ [R504] shichi routine. For complex arguments the algorithm is based on Mpmath’s [R505] shi and chi routines.

References

[R504](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html
[R505](1, 2) Fredrik Johansson and others. “mpmath: a Python library for arbitrary-precision floating-point arithmetic” (Version 0.19) http://mpmath.org/

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