相关论文: A recurrence relation for the odd order moments of…
This paper is devoted to the general theory of systems of time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
The time-ordered exponential of a time-dependent matrix $\mathsf{A}(t)$ is defined as the function of $\mathsf{A}(t)$ that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in…
Euler discovered a formula for expressing the value of the Riemann zeta function for all even positive integer arguments. A closed-form expression for the Riemann zeta function for all odd integer arguments, based on the values of the…
The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit representations of these functions. Taking advantage of their…
We describe a new framework for causal inference and its application to return time series. In this system, causal relationships are represented as logical formulas, allowing us to test arbitrarily complex hypotheses in a computationally…
A three term recurrence relation is derived for a basis consisting of polynomials multiplied by sines and cosines with large, but fixed frequencies. A numerical method for computing the coefficients of the three term recurrence relation is…
We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation for the involved univariate orthogonal polynomials, the…
In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…
In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…
This note simplifies the proof of a recent result on the oscillation of the prime product in Martens Theorem, and provides a quantitative expression for the error term. In addition, the corresponding oscillation results for the finite sums…
We explicitly solve a recurrence relation due to Feigin and Fuchs to obtain the Casimirs of the Virasoro algebra in terms of the inverse of the Shapovalov form. Combined with our recent result for the inverse Shapovalov form, this allows us…
The Cayley-Hamilton problem of expressing functions of matrices in terms of only their eigenvalues is well-known to simplify to finding the inverse of the confluent Vandermonde matrix. Here, we give a highly compact formula for the inverse…
The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…
Square matrices of the form $\widetilde{\mathbf{A}} =\mathbf{A} + \mathbf{e}D \mathbf{f}^*$ are considered. An explicit expression for the inverse is given, provided $\widetilde{\mathbf{A}}$ and $D$ are invertible with…
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator generating an iterative…
We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a…
In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. \ We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in…
We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…
Second order recurrence relations of real numbers arise form various applications in discrete time dynamical systems as well as in the context on Markov chains. Solutions to the recurrence relations are fully defined by the first two…