# Definition:Cosine Integral Function

## Definition

The cosine integral function is the real function $\Ci: \R_{>0} \to \R$ defined as:

$\map \Ci x = \displaystyle \int_{t \mathop = x}^{t \mathop \to +\infty} \frac {\cos t} t \rd t$

## Also defined as

Some sources give this as:

$\map \Ci x = \displaystyle -\int_{t \mathop = x}^{t \mathop \to +\infty} \frac {\cos t} t \rd t$

The difference between this and the definition given is trivial, but it is important to check results using this concept to confirm which version is being used.

## Also see

• Results about the cosine integral function can be found here.

## Sources

which gives the negated version