Related papers: Generalized Balancing and Balancing-Lucas numbers
We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. We study their properties, including relations, expressions and determinants. At the end in Appendix we derive first few expressions of these numbers.
In this article, we derive a congruence property of particular sum rules involving prime numbers. The resulting expression involves Bernoulli numbers and polynomials, for which we obtain, as a consequence, a general congruence relation as…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
Following the usual definition of $\lambda$-symmetries of differential equations, we introduce the analogous concept for difference equations and apply it to some examples.
This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…
Gaussian blur is a commonly-used method to filter image data. This paper introduces the collapsing sum, a new operator on matrices that provides a combinatorial interpretation of Gaussian blur. We study the combinatorial properties of this…
A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.
We introduce some generalizations of the Euler-Kronecker constant of a number field and study their arithmetic nature.
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
In this work, we made a generalization that includes all bicomplex Fibonacci-like numbers such as; Fibonacci, Lucas, Pell, etc.. We named this generalization as bicomplex Horadam numbers. For bicomplex Fibonacci and Lucas numbers we gave…
We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix…
In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.
Both Fibonacci and Lucas numbers can be described combinatorially in terms of 0-1 strings without consecutive ones. In the present article we explore the occupation numbers as well as the correlations between various positions in the…
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…
We give a simplified presentation of some results about recurrences of certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials.