  Inflationary cosmology has made significant strides in understanding the
physics driving the rapid expansion of the early universe. However, many
inflation models with diverse potential shapes present analysis, comparison,
and classification challenges. In this paper, we propose a novel approach to
tackle this issue. We introduce a general potential formula encompassing all
inflationary potentials, whether single-field or multi-field, into a single
mathematical framework. This formula establishes a unified framework for
systematically classifying inflation models based on their potential functions.
We showcase the efficacy of the general potential formula by successfully
reproducing well-known inflation models, such as the Starobinsky potential and
the Valley Hybrid Inflation model. Moreover, we derive general inflationary
parameters, including the slow-roll parameters and power spectra, using the
proposed formula. Our approach provides a versatile tool for classifying and
studying various inflationary scenarios, simplifying the analysis and
comparison of different models in the field of inflationary cosmology.
