Related papers: "Nice" Rational Functions
In this paper we deal with composite rational functions having zeros and poles forming consecutive elements of an arithmetic progression. We also correct a result published earlier related to composite rational functions having a fixed…
A sequence of functions {f_n(q)}_{n=1}^{\infty} satisfies the functional equation for multiplication of quantum integers if f_{mn}(q) = f_m(q)f_n(q^m) for all positive integers m and n. This paper describes the structure of all sequences of…
Having a function $f$ and a set of functionals $\{\mathcal{C}_{n}\}$, $c_n^f \equiv \mathcal{C}_n \left(f\right)$, one can interpret function approximation very generally as a construction of some function $\mathcal{A}_{N}^{f}$ such that…
We define two classes of functions, called regular (respectively, first-order) list functions, which manipulate objects such as lists, lists of lists, pairs of lists, lists of pairs of lists, etc. The definition is in the style of regular…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
Let h be a complex meromorphic function decomposed in two different ways P(f) and Q(g), where f, g are meromorphic functions and P, Q are rational functions. We follow an approach due to C.-C. Yang, P. Li and K. H. Ha who handle similar…
Generating functions for a fixed genus map and hypermap enumeration become rational after a simple explicit change of variables. Their numerators are polynomials with integer coefficients that obey a differential recursion, and denominators…
The aim of this paper is to provide sufficient conditions for when a polynomial or rational function over a field K is prime using its order of vanishing at infinity and the resultant.
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
For positive integers m and n, denote S(m,n) as the associated Stirling number of the second kind and let z be a complex variable. In this paper, we introduce the Stirling functions S(m,n,z) which satisfy S(m,n,z) = S(m,n) for any z which…
For any positive integer n, a new family of periodic functions in power series form and of period n is used to solve in closed form a class of polynomial equation of order n. The n roots are the values of the appropriate function from that…
In this note we axiomatize the classes of rudimentary functions, primitive recursive functions, safe recursive set functions, and predicatively computable functions.
It is well known that sin(a\pi/b), cos(a\pi/b), etc., are only rational numbers for a few select integers a and b. We show that this is equivalent to the fact that only for d = 1,2,3,4, and 6 is the primitive dth root of unity of degree 2…
We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…
For each odd prime power q, we construct an infinite sequence of rational functions f(X) in F_q(X), each of which is exceptional, which means that for infinitely many n the map c-->f(c) induces a bijection of P^1(F_{q^n}). Moreover, each of…
In this paper, we consider rational functions $f$ with some minor restrictions over the finite field $\mathbb{F}_{q^n},$ where $q=p^k$ for some prime $p$ and positive integer $k$. We establish a sufficient condition for the existence of a…
The paper gives some criteria for partial sums of rational number sequences to be not rational functions and to be not algebraic functions. As an application, we study partial sums of some famous rational number sequences in mathematical…
For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.
A class of rational functions characterized by some wonderful properties is studied. The properties that identify this class include simple algebra (their inverses can be expressed in radicals), simple topology (the total space of the…