For the sake of completeness and because it serves as a good introduction to the derivation of the functional equation satisfied by the generating function of s n, we first derive the well-known functional equation satisfied by the generating function of the t n.
In fact, this new generalization is defined by the generating function as the equality f S, v ( t ; a, b ; γ ) = ( γ b t − a t ) v v !
The profiles of the degree of polymerization, polydispersity, degree of branching, and structural units of the hyperbranched polymers with the conversions were all calculated by the generating function method.
The changes of the degree of polymerization, polydispersity, degree of branching, and structural units of the hyperbranched polymers with the conversions were all investigated by the generating function method.
Sheffer sequences are characterized by the generating function [7], Theorem 2.3.4].
Sheffer sequences are characterized by the generating function of [[1], Theorem 2.3.4].
If we take, then the classical Euler polynomials are defined by the generating function, (1.8).
The weighted -Bernoulli polynomials are also defined by the generating function as follows: (1.9).
The Bernoulli numbers and polynomials are defined by the generating function as (1.2). (1.3).
and the second Stirling number is defined by the generating function to be ( e t − 1 ) n = n !
Let F z) be given by the generating function with the moments f n =w H A n u.
