scipy.special.sici

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

Sine and cosine integrals.

The sine integral is

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

and the cosine integral is

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

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 sine and cosine integrals.

outtuple of ndarray, optional

Optional output arrays for the function results

Returns

siscalar or ndarray

Sine integral at x

ciscalar or ndarray

Cosine integral at x

Notes

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

For real arguments the function is computed by calling Cephes’ [1] sici routine. For complex arguments the algorithm is based on Mpmath’s [2] si and ci 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/