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The most common line shapes in EPR are Gaussian and Lorentzian. In addition, Dysonians and Voigtians are used.

Gaussian

The formula for a Gaussian absorption lineshape normalized so that its integral is 1 is

where x_{0} is the line centre and
is
the distance between the inflection points. It
is related to the FWHM (full width at half height) via

At the center x_{0} the value of the Gaussian is

The first derivative has a peak-to-peak distance of .

The integral of the Gaussian lineshape function is

Lorentzian

The formula for a Lorentzian absorption lineshape normalized so that its integral is 1 is

where x_{0} is the center and
is
the distance between the inflection points. It
is related to the FWHM (full width at half height) via

At the center x_{0} the value of the Lorentzian is

The first derivative has a peak-to-peak distance of .

The integral of the Lorentzian lineshape function is

Voigtian and Pseudovoigtian

The Voigt line shape is the convolution of Lorentzian and a Gaussian line shape. It cannot be expresed in closed analytical form. It can be approximated by a linear combination of a Lorentzian and a Gaussian, a so-called pseudo-Voigt function.