Exponential generating functions So far, we defined the generating function for a sequence $\left (h_n\right)_ {n \geq 0}$ by using the monomials $1, x, x^2, \ldots$ There were no coefficient ...

Here presented is constructive generalization of exponential Euler polynomial and exponential splines based on the interrelationship between the set of concepts of Eulerian polynomials, Eulerian ...

Abstract: Generating functions (GFs) are one of the most useful tools for problem solving, as they have been playing an important role in many applications, including but not limited to counting, ...

The Dirichlet series L m (s) are of fundamental importance in number theory. Shanks defined the generalized Euler and class numbers in connection with the Dirichlet series, denoted by {s m,n } n≥0 .

An exponential generating function of correlators is calculated explicitly for the sl2 Gaudin model (degenerated quantum integrable XXX spin chain). The calculation relies on the Gauss decomposition ...

Exponential generating functions So far, we defined the generating function for a sequence $\left (h_n\right)_ {n \geq 0}$ by using the monomials $1, x, x^2, \ldots$ There were no coefficient ...