  A cosmologically viable hypergeometric model in the modified gravity theory
$f(R)$ is found from the need for asintoticity towards $\Lambda$CDM, the
existence of an inflection point in the $f(R)$ curve, and the conditions of
viability given by the phase space curves $(m, r)$, where $m$ and $r$ are
characteristic functions of the model. To analyze the constraints associated
with the viability requirements, the models were expressed in terms of a
dimensionless variable, i.e. $R\to x$ and $f(R)\to y(x)=x+h(x)+\lambda$, where
$h(x)$ represents the deviation of the model from General Relativity. Using the
geometric properties imposed by the inflection point, differential equations
were constructed to relate $h'(x)$ and $h''(x)$, and the solutions found were
Starobinsky (2007) and Hu-Sawicki type models, nonetheless, it was found that
these differential equations are particular cases of a hypergeometric
differential equation, so that these models can be obtained from a general
hypergeometric model. The parameter domains of this model were analyzed to make
the model viable.
