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 principal branch of the logarithm.

Parameters

xarray_like

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

outtuple of ndarray, optional

Optional output arrays for the function results

Returns

siscalar or ndarray

Hyperbolic sine integral at x

ciscalar or 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’ [1] shichi routine. For complex arguments the algorithm is based on Mpmath’s [2] shi and chi routines.

References

1

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/

2

Fredrik Johansson and others. “mpmath: a Python library for arbitrary-precision floating-point arithmetic” (Version 0.19) http://mpmath.org/