4 citations · 5 across the 3 of their papers we have counts for
4 papers
A generating function for the Euler numbers of the second kind and its application
Dmitry V. Kruchinin, Vladimir V. Kruchinin
In the paper, 2 explicit formulas for the Euler numbers of the second kind are obtained. Based on those formulas a exponential generating function is deduced. Using the generating…
Method for solving an iterative functional equation
Dmitry Kruchinin, Vladimir Kruchinin
Using the notion of the composita, we obtain a method of solving iterative functional equations of the form , where , . We pro…
Integer properties of a composition of exponential generating functions
Dmitry Kruchinin
In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite num…
Application of a composition of generating functions for obtaining explicit formulas of polynomials
Vladimir Kruchinin, Dmitry Kruchinin
Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated L…