@staticmethod<EOL><INDENT>def Twu(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*((T/Tc)**(c3*(c2 - <NUM_LIT:1>))*exp(c1*(-(T/Tc)**(c2*c3) + <NUM_LIT:1>)))<EOL>if not full:<EOL><INDENT>return a_alpha<EOL><DEDENT>else:<EOL><INDENT>da_alpha_dT = a*(-c1*c2*c3*(T/Tc)**(c2*c3)*(T/Tc)**(c3*(c2 - <NUM_LIT:1>))*exp(c1*(-(T/Tc)**(c2*c3) + <NUM_LIT:1>))/T + c3*(T/Tc)**(c3*(c2 - <NUM_LIT:1>))*(c2 - <NUM_LIT:1>)*exp(c1*(-(T/Tc)**(c2*c3) + <NUM_LIT:1>))/T)<EOL>d2a_alpha_dT2 = a*(c3*(T/Tc)**(c3*(c2 - <NUM_LIT:1>))*(c1**<NUM_LIT:2>*c2**<NUM_LIT:2>*c3*(T/Tc)**(<NUM_LIT:2>*c2*c3) - c1*c2**<NUM_LIT:2>*c3*(T/Tc)**(c2*c3) - <NUM_LIT:2>*c1*c2*c3*(T/Tc)**(c2*c3)*(c2 - <NUM_LIT:1>) + c1*c2*(T/Tc)**(c2*c3) - c2 + c3*(c2 - <NUM_LIT:1>)**<NUM_LIT:2> + <NUM_LIT:1>)*exp(-c1*((T/Tc)**(c2*c3) - <NUM_LIT:1>))/T**<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 Twu et al. (1991) [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 = \left(\frac{T}{Tc}\right)^{c_{3} \left(c_{2} 
            - 1\right)} e^{c_{1} \left(- \left(\frac{T}{Tc}
            \right)^{c_{2} c_{3}} + 1\right)}

        References
        ----------
        .. [1] Twu, Chorng H., David Bluck, John R. Cunningham, and John E. 
           Coon. "A Cubic Equation of State with a New Alpha Function and a 
           New Mixing Rule." Fluid Phase Equilibria 69 (December 10, 1991): 
           33-50. doi:10.1016/0378-3812(91)90024-2.