arXiv subjects

Vladimir V. Kruchinin

Publications and source records attributed to Vladimir V. Kruchinin.

3 recordsLinked to original sources

arXiv2024

Identities and Generating Functions of Products of Generalized Fibonacci numbers, Catalan and Harmonic Numbers

We considered the properties of generalized Fibonacci and Lucas numbers class. The analogues of well-known Fibonacci identities for generalized numbers are obtained. We gained a new identity of product convolution of generalized Fibonacci and Lucas numbers. We wrote down generating functions of generalized Fibonacci and Lucas numbers products, their multisections, harmonic numbers and Catalan numbers.

math.CO↗

arXiv2018

A generating function for the Euler numbers of the second kind and its application

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 function some well-known and new identities for the Euler number of the second kind are obtained.

math.CO↗

arXiv2013

Composita and its properties

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 $n$ is introduced and is termed composita. We present theorems about compositae and operations with compositae. We obtain the compositae of polynomials, trigonometric and hyperbolic functions. Using the notion of the composita we get the solution of the functional equation $B(x)=H(xB(x)^m)$, where $H(x),B(x)$ are generating functions, and $m\in \mathbb{N}$.

math.CO↗