Related papers: On the Recurrence Formula for Fixed Points of the …
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
This paper presents the equality of finite index sums of Bessel func- tions containing arbitrary numbers of terms. These reduce to the familiar three term recursion formulas in simple cases.
In this paper we investigate fixed-point numbers and entropies of endomorphisms on abelian varieties. It was shown quite recently that the number of fixed-points of an iterated endomorphism on a simple complex torus is either periodic or…
We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point…
The implementation of an algorithm for three-loop massive vacuum integrals, based on the explicit solution of the recurrence relations, in REDUCE and FORM is described.
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras…
Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence…
The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence…
We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…
In this paper, we present a fixed point method for high-precision computation of number $\pi$ based on the sine function. Let $P\in \mathbb{N}$. We define the function: \[ S\left(x\right) =x+\sum_{k=1}^{P}\left(\prod_{\ell=1}^{k-1}\frac…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements…
This paper introduces a formal notion of fixed point explanations, inspired by the "why regress" principle, to assess, through recursive applications, the stability of the interplay between a model and its explainer. Fixed point…
In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…
We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…
We define the excedance number on the complex reflection groups and compute its multidistribution with the number of fixed points on the set of involutions in these groups. We use some recurrence formulas and generating functions…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…