Related papers: Generalized matrix functions on a linear sum of pe…
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
We show that the permanent of a matrix is a linear combination of determinants of block diagonal matrices which are simple functions of the original matrix. To prove this, we first show a more general identity involving \alpha-permanents:…
In this paper, we give some determinantal and permanental representations of Generalized Lucas Polynomials by using various Hessenberg matrices, which are general form of determinantal and permanental representations of ordinary Lucas and…
This paper defines the Iris function and provides two formulations of the matrix permanent. The first formulation, valid for arbitrary complex matrices, expresses the permanent of a complex matrix as a contour integral of a second order…
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…
In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.
In matrix theory and numerical analysis there are two very famous and important results. One is Gersgorin circle theorem, the other is strictly diagonally dominant theorem. They have important application and research value, and have been…
A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
In this paper we study generalized J-inner matrix valued functions which appear as resolvent matrices in various indefinite interpolation problems. Reproducing kernel indefinite inner product spaces associated with a generalized J-inner…
Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times…
The recurrence matrix relations, differentiation formulas, and analytical and fractional integral properties of incomplete gamma matrix functions $\gamma(Q, x)$ and $\Gamma(Q, x)$ are all covered in this article. The generalized incomplete…
In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
Often in mathematics it is useful to summarize a multivariate phenomenon with a single number and in fact, the determinant -- which is represented by det -- is one of the simplest cases. In fact, this number it is defined only for square…
In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.
Extending a classical estimate of Mertens for the sum of the reciprocals of the first primes, we provide an explicit remainder formula for products of an arbitrary, but fixed, number of primes.
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on…