Properties of a Composition of Exponential and Ordinary Generating Functions - Kruchinin, Dmitry V.; Shablya, Yuriy V.; Kruchinin, Vladimir V.; Shelupanov, Alexander A. (Communications in Mathematics and Applications, 2018)
In this paper, we consider the composition of ordinary and exponential generating functions. The obtained property of the composition of ordinary and exponential generating functions can be used for distinguishing prime numbers from composite numbers. For example, it can be applied for constructing new probabilistic primality criteria. Using the obtain property, we get several congruence relations for the Uppuluri-Carpenter, Euler, and Fubini numbers.
Keywords: Generating function; composition; composita; primality criterion; Euler number