docs: def Gamma1_gasrad(beta):
      ''' 
      Gamma1 for a mix of ideal gas and radiation
  
      Hansen & Kawaler, page 177, Eqn. 3.110
      
      Parameters
      ----------
      beta : float
          Gas pressure fraction Pgas/(Pgas+Prad)
  
      '''
      Gamma3minus1 = (old_div(2.,3.))*(4.-3.*beta)/(8.-7.*beta) 
      Gamma1 = beta + (4.-3.*beta) * Gamma3minus1
      return Gamma1