  In [10] Jain introduced the modified form of the Sz\'asz-Mirakjan operator,
based on certain parameter $0\le\beta<1$. Several modifications of the
operators are available in the literature. Here we consider actual Durrmeyer
variant of the operators due to [10]. It is observed here that the Durrmeyer
variant has the nice properties and one need not to take any restriction on
$\beta$ in order to get convergence. We establish moments using the Tricomi's
confluent hypergeometric function and Stirling numbers of first kind, also
estimate some direct results
