20 citations · 34 across the 8 of their papers we have counts for
9 papers
A Family of Generating Functions for Reciprocal Binomial Coefficients and Its Applications
Dmitry Kruchinin, Vladimir Kruchinin
A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal bino…
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…
Explicit formulas for enumeration of lattice paths: basketball and the kernel method
Cyril Banderier, Christian Krattenthaler, Alan Krinik +4
This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude and ending at a given altitude ,…
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…
The method for obtaining expressions for coefficients of reverse generating functions
Vladimir Kruchinin
The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer , called compo…
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…
A Method for Obtaining Generating Function for Central Coefficients of Triangles
Vladimir Kruchinin, Dmitry Kruchinin
We present techniques for obtaining a generating function for the central coefficients of a triangle , which is given by the expression $[xH(x)]^k=\sum_{n\geqslant k} T(n,k…
Derivation of Bell Polynomials of the Second Kind
Vladimir Kruchinin
New methods for derivation of Bell polynomials of the second kind are presented. The methods are based on an ordinary generating function and its composita. The relation between a…
Composita and its properties
Vladimir V. Kruchinin, Dmitry V. Kruchinin
In this paper we study the coefficients of the powers of an ordinary generating function and their properties. A new class of functions based on compositions of an integer is i…