Convergence of operators based on some special functions

The present article is in continuation of our previous paper by Gupta (Rev Real Acad Cienc Exactas Fis Nat Ser A-Mat 118:19, 2024, https://doi.org/10.1007/s13398-023-01521-8), we consider the operators, which are connected to the solutions of differential equations. The differential equations considered here are Hermite and Laguerre differential equations. We discuss here the new operators constructed by the solutions of these differential equations. We also provide only the basic convergence properties. As other can be done by researchers in different settings. In the last section, we provide higher order self composition operators and observe that the convergence takes place for all finite higher order composition operators but worse convergence is achieved in case of higher order finite self composition of operators.