\[A(x)=a_0+a_1\cdot x+\tfrac12\cdot a_2\cdot x^2+\dots+\tfrac1{n!}\cdot a_n\cdot x^n+\dots\] is called the \index{exponential generating function}\emph{exponential ...

The relation in (6) will be exploited in this paper to derive exact expressions and some recurrence relations for the moment generating functions of from the Erlang-truncated exponential distribution.

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, identity ...

In the sixth chapter of his notebooks Ramanujan introduced a method of summing divergent series which assigns to the series the value of the associated Euler-MacLaurin constant that arises by applying ...

upper left corner sub matrix of a given infinite matrix by introducing Exponential Generating functions of some sequences. and how to get a sequence by calculating the determinant of n x n upper left ...

We study a symmetric generalization p(k)((N)) (eta, alpha) of the binomial distribution recently introduced by Bergeron et al., where eta is an element of[0,1] denotes the win probability and alpha is ...

In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential ...