Moment estimations of new Szász–Mirakyan–Durrmeyer operators

Jain (1972) introduced the modified form of the Szász–Mirakjan operator, based on certain parameter 0 ≤ β < 1. Several modifications of the operators proposed and are available in the literature. Here we consider actual Durrmeyer variants of the operators due to Jain. It is observed here that the Durrmeyer variant have nice properties and one need not to take any restriction on β in order to obtain convergence. We establish moments using the Tricomi’s confluent hypergeometric function and Stirling numbers of first kind, and also estimate some direct results.