Related papers: A new operational matrix based on Bernoulli polyno…
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.
General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…
We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials. As applications, we give interesting examples. In…
In this paper, we prove new identities for Bernoulli polynomials that extend Alzer and Kwong's results. The key idea is to use the Volkenborn integral over $\mathbb Z_p$ of the Bernoulli polynomials to establish recurrence relations on the…
Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications including optics and atmospheric sciences. In this paper, we…
Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…
We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbral Calculus associated with it. Also, we present…
Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operators to be invertible are obtained; so that the main results in the…
We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to…
In this paper, we derive new matrix representation for Daehee numbers and polynomials, the lambda-Daehee numbers and polynomials and the twisted Daehee numbers and polynomials. This helps us to obtain simple and short proofs of many…
Burchnall and Chaundy showed that if two ODOs $P$, $Q$ with analytic coefficients commute there exists a polynomial $f(\lambda ,\mu)$ with complex coefficients such that $f(P,Q)=0$, called the BC-polynomial. This polynomial can be computed…
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
We consider the vector space of $n \times n$ matrices over $\mathbb C$, Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these operators are studied with respect to the underlying…