Thompson-cox-hastings Pseudo-voigt Function 📥

# Normalized Gaussian & Lorentzian with FWHM = G_V sigma = G_V / (2*sqrt(2*log(2))) # Gaussian sigma gamma = G_V / 2 # Lorentzian half-width at half-max t = (x - x0)

G = (1/(sigma*sqrt(2*pi))) * exp(-0.5*(t/sigma)**2) L = (gamma/pi) / (t**2 + gamma**2) thompson-cox-hastings pseudo-voigt function

[ \Gamma_V = \left( \Gamma_G^5 + 2.69269 , \Gamma_G^4 \Gamma_L + 2.42843 , \Gamma_G^3 \Gamma_L^2 + 4.47163 , \Gamma_G^2 \Gamma_L^3 + 0.07842 , \Gamma_G \Gamma_L^4 + \Gamma_L^5 \right)^1/5 ] # Normalized Gaussian & Lorentzian with FWHM =

The is:

[ V_\textTCH(x) = \eta , L(x) + (1-\eta) , G(x) ] \Gamma_G^4 \Gamma_L + 2.42843