In mathematics, the

The different sine integral definitions are:

In signal processing, the oscillations of the Sine integral cause overshoot and ringing artifacts when using the sinc filter, and frequency domain ringing if using a truncated sinc filter as a low-pass filter.

The Gibbs phenomenon is a related phenomenon: thinking of sinc as a low-pass filter and the Sine integral as its convolution with the Heaviside step function, it corresponds to truncating the Fourier series, which causes the Gibbs phenomenon.

The different cosine integral definitions are:

The spiral formed by parametric plot of si,ci is known as Nielsen's spiral. It is also referred to as the Euler spiral, the Cornu spiral, a clothoid, or as a linear-curvature polynomial spiral. The spiral is also closely related to the Fresnel integrals. This spiral has applications in vision processing, road and track construction and other areas.

Cases of imaginary argument of the generalized integro-exponential function are

**trigonometric integrals**are a family of integrals which involve trigonometric functions. A number of the basic trigonometric integrals are discussed at the list of integrals of trigonometric functions.## Sine integral

In signal processing, the oscillations of the Sine integral cause overshoot and ringing artifacts when using the sinc filter, and frequency domain ringing if using a truncated sinc filter as a low-pass filter.

The Gibbs phenomenon is a related phenomenon: thinking of sinc as a low-pass filter and the Sine integral as its convolution with the Heaviside step function, it corresponds to truncating the Fourier series, which causes the Gibbs phenomenon.

## Cosine integral

## Hyperbolic sine integral

The hyperbolic sine integral:## Hyperbolic cosine integral

The hyperbolic cosine integral:## Nielsen's spiral

## Expansion

Various expansions can be used for evaluation of Trigonometric integrals, depending on the range of the argument.### Asymptotic series (for large argument)

### Convergent series

## Relation with the exponential integral of imaginary argument

The functionCases of imaginary argument of the generalized integro-exponential function are

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