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The estimations of lower order $\left(R\right)$ $\lambda$ in terms of the sequences $\left\{a_n\right\}$ and $\left\{{\lambda }_n\right\}$ for an entire Dirichlet series $f\left(s\right)={\sum }_{n=1}^{\infty }{a}_n{e}^{s\lambda n}$, have been obtained, namely : $$\begin{array}{cc}\hfill \lambda & =\underset{\left\{{\lambda }_{n_p}\right\}}{max}lim\underset{p\to \infty }{inf}\frac{{\lambda }_{n_p}log{\lambda }_{n_{p-1}}}{log|a_{n_p}{|}^{-1}}\hfill \\ & =\underset{\left\{{\lambda }_{n_p}\right\}}{max}lim\underset{p\to \infty }{inf}\frac{({\lambda }_{n_p}-{\lambda }_{n_{p-1}})log{\lambda }_{n_{p-1}}}{log\left|a_{n_{p-1}}\right|a_{n_p}|}.\hfill \end{array}$$ One of these estimations improves considerably the estimations earlier obtained by Rahman (Quart. J. Math. Oxford, (2), 7, 96-99 (1956)) and Juneja and Singh (Math. Ann., 184(1969), 25-29 ).