Appendix C. List of functions

To simplify equations, following substitution is introduced:

 
       t = (x - a1) / a2

where a1 is a position of peak's center and a2 is a HWHM.

Equation C.1. Gaussian (^G)

 
       Type in program "s.i ^G" to see formula.

Equation C.2. Lorentzian (^L)

 
       Type in program "s.i ^L" to see formula.

Equation C.3. Pearson VII (^P)

 
       Type in program "s.i ^P" to see formula.

Equation C.4. Pseudo-Voigt (^S)

 
       Type in program "s.i ^S" to see formula.

a3 parameters in Pearson VII and Pseudo-Voigt are not related.

Equation C.5. Voigt (^V)

 
       Type in program "s.i ^V" to see formula.

Voigt function is a convolution of Gaussian and Lorentzian functions. a0 = heigth, a1 = center, a2 is proportional to the Gaussian width, and a3 is proportional to the ratio of Lorentzian and Gaussian widths. And t is just a variable of integration. Voigt is computed according to R.J.Wells, “ Rapid approximation to the Voigt/Faddeeva function and its derivatives ”, Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 29-48. (See also: http://personalpages.umist.ac.uk/staff/Bob.Wells/voigt.html). Is the approximation exact enough for all possible uses of fityk program?

Equation C.6. Polynomial (^n)

 
       Type in program "s.i ^n" to see formula.