4, by using generating functions associated with trigonometric functions and the central factorial numbers of the second kind, we derive identities related to the central factorial numbers of the second kind, the array polynomials, and combinatorial sum.
In this paper, we study the ordinary differential equations associated with the generating function of general modified degenerate Euler numbers.
Shahrezaei and Swain [ 55] showed that in the same limit of time scale separation, one can obtain the exact joint probability distribution of mRNA and protein fluctuations by solving the generating function equation associated with the CME of the full network.
Very recently, Srivastava [9], motivated essentially by recent works of several authors, presented a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associated with various classes of the extended Hurwitz-Lerch zeta functions (see also the references in [9]).
We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions.
Let be the generating functions of defined by (3.3).
We associate to ψ, d, N the polynomials P n, ψ, d ( x, ξ N ) defined by the generating function ∑ n ≥ 0 P n, ψ, d ( x, ξ N ) t n n !
We construct generating functions for the Bernstein type basis functions explicitly by the following theorem.
Order is determined by generating function.
By using a generating function, we derive various performance indices.
