Some Generalization of the Theory of Generating Functions

The author invites readers to consider some very unusual methods of calculations that he performed while solving the problem of analytic continuation of the Riemann function containing the critical strip inside of which there is an infinite set of nontrivial zeros of function by B. Rieman's hypothesis. Similar methods are used by the author when studying the properties of the generating function of Hermite polynomials with a nonnegative integer exponent.