The paper describes establishment of bounding inequalities for the Jacobi function as a consequence of reasonably sharp inequalities for the classical Laguerre functions, given in Section 2 of the paper in the form of four lemmas. By virtue of hypergeometric representations of the classical Jacobi function

${P}_{\upsilon}^{(\alpha ,\beta )}\left(z\right)$ $(\upsilon \in C)$ of the first kind and the classical Laguerre function

${L}_{\upsilon}^{\left(\mu \right)}\left(z\right)$ $(\upsilon \in C)$ in terms of

${}_{1}{F}_{1}(\xb7)$, the Eulerian integral is written and then appealing to the corresponding version of Love’s inequality, the first bounding inequality is obtained. Further, the lemmas those given in Section 2 are employed to obtain remaining two bounding inequalities.