Related papers: On an identity derived from interpolation theory
The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix…
An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…
In this paper, we study linear differential equations arising from Bessel polynomials and their applications. From these linear differential equations, we give some new and explicit identities for Bessel polynomials.
The class $Ts(r,f)$ the trigonometric interpolation splines depending on the parameter vectors, selected convergence factors and interpolation factors is considered. The main properties of simple interpolation trigonometric splines are…
In this note, we present several identities involving binomial coefficients and the two kind of Stirling numbers.
We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…
This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion…
In this article we obtain a general polynomial identity in $k$ variables, where $k\geq 2$ is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of the powers of a $k \times k$ matrix.…
Combining Newton and Lagrange interpolation, we give $q$-identities which generalize results of Van Hamme, Uchimura, Dilcher and Prodinger.
In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
In this article we shows some results about algebra with the group of units having special polynomial identity.
On the basis of the generalizations of the Jacobi identity found by the author some identities satisfied by the curvature and torsion of a covariant differentiation are derived. A kind of the generalized covariant differentiation is…
We study and derive identities for the multi-variate independence polynomials from the perspective of heaps theory. Using the inversion formula and the combinatorics of partially commutative algebras we show how the multi-variate version of…
In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…
We give a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by product, we obtain a simple proof of an interesting…
Classical binomial identities are established by giving probabilistic interpretations to the summands. The examples include Vandermonde identity and some generalizations.
This is a straightforward introduction to the properties of polynomials in many variables that do not vanish in the open upper half plane. Such polynomials generalize many of the well-known properties of polynomials with all real roots.
Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…
We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.