"generalized to include" is a correct and usable phrase in written English.
It is typically used to describe when something becomes more broad and encompassing, including a wider range of people, ideas, or concepts. Example: "Over time, the term 'family' has been generalized to include not only traditional nuclear families, but also single-parent households, same-sex couples, and chosen families."
The first law of thermodynamics is the energy conservation principle of mechanics (i.e., for all changes in an isolated system, the energy remains constant) generalized to include heat.
The theory is generalized to include what others would touch, see, and hear as well, so that what the realists call "public" will also be defined in terms of the coherence of perceptions.
The theory is then generalized to include any dth-order fixed point of the system.
Besides, the approach is generalized to include different viewing angles on the human form.
This theory has been presently generalized to include the initial stresses in the composite and to accommodate the eigenstresses which include the damage variables.
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder.
Sensitivities are normalized with respect to that of the harmonic oscillator, and generalized to include the mode vectors through the definition of a figure of merit.
The governing equation of motion is derived by the minimization of the Hamiltonian and generalized to include the viscous damping effect.
Certainly, the public good decision function was generalized to include that of the MDP Procedure, whereas, the distributional vector was fixed to the above specific value.
While the nonlinear Fourier method is specifically applied to the NLS equation, the approach is easily generalized to include the class of spectral problems due to Ablowitz, Kaup, Newell, and Segur (AKNS).
The treatment of Hoult (1972. Annual Review of Fluid Mechanics, 4, 341 368) is generalized to include the case where the volume of an oil strip is not necessarily constant and varies as a power-law function of time.
