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An attempt is made to introduce and use operational techniques to study about a new sequence of functions containing generalized Jacobi polynomial. Some generating relations, finite summation formulae, explicit representation of a sequence of function $S_{n,\tau ,k}^{(\alpha ,\beta ,\gamma ,\delta )} (x;a,u,v)$ associated with the generalized Jacobi polynomial $P_{n,\,\tau }^{\left( {\alpha ,\,\gamma ,\,\beta } \right)} (x)$ have been deduced.