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 principle branch of the logarithm.

Parameters:

x : array_like

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

Returns:

si : ndarray

Sine integral at x

ci : 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’ [R516] sici routine. For complex arguments the algorithm is based on Mpmath’s [R517] si and ci routines.

References

[R516]

(1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

[R517]

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