  The aim of this paper is to study generating functions for the coefficients
of the classical superoscillatory function associated with weak measurements.
We also establish some new relations between the superoscillatory coefficients
and many well-known families of special polynomials, numbers, and functions
such as Bernstein basis functions, the Hermite polynomials, the Stirling
numbers of second kind, and also the confluent hypergeometric functions.
Moreover, by using generating functions, we are able to develop a recurrence
relation and a derivative formula for the superoscillatory coefficients.
