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 cosint
 cosine integral

 Calling Sequence cosint(x)

Parameters

 x - expression

Description

 • The cosine integral is defined for all complex x as follows:

$\mathrm{\gamma }+\mathrm{ln}\left(x\right)+{{\int }}_{0}^{x}\frac{\mathrm{cos}\left(t\right)-1}{t}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}t$

 • When x is a container object such as an Array or list, the cosint(x) function computes the element-wise cosine integral of x.  For example when x is a Matrix the result R is formed as R[i,j] = Ci(x[i,j]).
 • When x is numeric, cosint(x) is equivalent to Ci(x).

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $x≔\mathrm{Matrix}\left(2,3,'\mathrm{fill}'=-3+I\right):$
 > $\mathrm{cosint}\left(x\right)$
 $\left[\begin{array}{ccc}{\mathrm{Ci}}{}\left({3}{-}{I}\right){+}{I}{}{\mathrm{π}}& {\mathrm{Ci}}{}\left({3}{-}{I}\right){+}{I}{}{\mathrm{π}}& {\mathrm{Ci}}{}\left({3}{-}{I}\right){+}{I}{}{\mathrm{π}}\\ {\mathrm{Ci}}{}\left({3}{-}{I}\right){+}{I}{}{\mathrm{π}}& {\mathrm{Ci}}{}\left({3}{-}{I}\right){+}{I}{}{\mathrm{π}}& {\mathrm{Ci}}{}\left({3}{-}{I}\right){+}{I}{}{\mathrm{π}}\end{array}\right]$ (1)