@staticmethod<EOL><INDENT>def Coquelet(self, T, full=True, quick=True):<DEDENT>
c1, c2, c3 = self.alpha_function_coeffs<EOL>T, Tc, a = self.T, self.Tc, self.a<EOL>a_alpha = a*(exp(c1*(-T/Tc + <NUM_LIT:1>)*(c2*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:2> + c3*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>)**<NUM_LIT:2>))<EOL>if not full:<EOL><INDENT>return a_alpha<EOL><DEDENT>else:<EOL><INDENT>da_alpha_dT = a*((c1*(-T/Tc + <NUM_LIT:1>)*(-<NUM_LIT:2>*c2*sqrt(T/Tc)*(-sqrt(T/Tc) + <NUM_LIT:1>)/T - <NUM_LIT:3>*c3*sqrt(T/Tc)*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:2>/T)*(c2*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:2> + c3*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>) - c1*(c2*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:2> + c3*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>)**<NUM_LIT:2>/Tc)*exp(c1*(-T/Tc + <NUM_LIT:1>)*(c2*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:2> + c3*(-sqrt(T/Tc) + <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>)**<NUM_LIT:2>))<EOL>d2a_alpha_dT2 = a*(c1*(c1*(-(c2*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:2> - c3*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>)/Tc + sqrt(T/Tc)*(-<NUM_LIT:2>*c2 + <NUM_LIT:3>*c3*(sqrt(T/Tc) - <NUM_LIT:1>))*(sqrt(T/Tc) - <NUM_LIT:1>)*(T/Tc - <NUM_LIT:1>)/T)**<NUM_LIT:2>*(c2*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:2> - c3*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>)**<NUM_LIT:2> - ((T/Tc - <NUM_LIT:1>)*(c2*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:2> - c3*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>)*(<NUM_LIT:2>*c2/Tc - <NUM_LIT:6>*c3*(sqrt(T/Tc) - <NUM_LIT:1>)/Tc - <NUM_LIT:2>*c2*sqrt(T/Tc)*(sqrt(T/Tc) - <NUM_LIT:1>)/T + <NUM_LIT:3>*c3*sqrt(T/Tc)*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:2>/T) + <NUM_LIT:4>*sqrt(T/Tc)*(<NUM_LIT:2>*c2 - <NUM_LIT:3>*c3*(sqrt(T/Tc) - <NUM_LIT:1>))*(sqrt(T/Tc) - <NUM_LIT:1>)*(c2*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:2> - c3*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>)/Tc + (<NUM_LIT:2>*c2 - <NUM_LIT:3>*c3*(sqrt(T/Tc) - <NUM_LIT:1>))**<NUM_LIT:2>*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:2>*(T/Tc - <NUM_LIT:1>)/Tc)/(<NUM_LIT:2>*T))*exp(-c1*(T/Tc - <NUM_LIT:1>)*(c2*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:2> - c3*(sqrt(T/Tc) - <NUM_LIT:1>)**<NUM_LIT:3> + <NUM_LIT:1>)**<NUM_LIT:2>))<EOL>return a_alpha, da_alpha_dT, d2a_alpha_dT2<EOL><DEDENT>
r'''Method to calculate `a_alpha` and its first and second
        derivatives according to Coquelet et al. (2004) [1]_. Returns `a_alpha`, `da_alpha_dT`, and 
        `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives` for more 
        documentation. Three coefficients needed.

        .. math::
            \alpha = e^{c_{1} \left(- \frac{T}{Tc} + 1\right) \left(c_{2} 
            \left(- \sqrt{\frac{T}{Tc}} + 1\right)^{2} + c_{3} 
            \left(- \sqrt{\frac{T}{Tc}} + 1\right)^{3} + 1\right)^{2}}

        References
        ----------
        .. [1] Coquelet, C., A. Chapoy, and D. Richon. "Development of a New 
           Alpha Function for the Peng–Robinson Equation of State: Comparative 
           Study of Alpha Function Models for Pure Gases (Natural Gas 
           Components) and Water-Gas Systems." International Journal of 
           Thermophysics 25, no. 1 (January 1, 2004): 133-58. 
           doi:10.1023/B:IJOT.0000022331.46865.2f.