Log in

Relevant bibliographies by topics / Recurrence sequences with nonconstant coefficients

Contents

Journal articles

Academic literature on the topic 'Recurrence sequences with nonconstant coefficients'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Recurrence sequences with nonconstant coefficients.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Recurrence sequences with nonconstant coefficients"

1

van der Poorten, A. J., and I. E. Shparlinski. "On linear recurrence sequences with polynomial coefficients." Glasgow Mathematical Journal 38, no. 2 (1996): 147–55. http://dx.doi.org/10.1017/s0017089500031372.

Full text

Abstract:

We consider sequences (Ah)defined over the field ℚ of rational numbers and satisfying a linear homogeneous recurrence relationwith polynomial coefficients sj;. We shall assume without loss of generality, as we may, that the sj, are defined over ℤ and the initial values A0A]…, An−1 are integer numbers. Also, without loss of generality we may assume that S0 and Sn have no non-negative integer zero. Indeed, any other case can be reduced to this one by making a shift h → h – l – 1 where l is an upper bound for zeros of the corresponding polynomials (and which can be effectively estimated in terms of their heights)

APA, Harvard, Vancouver, ISO, and other styles

2

Rebenda, Josef, and Zuzana Pátíková. "Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays." Complexity 2020 (February 28, 2020): 1–12. http://dx.doi.org/10.1155/2020/2854574.

Full text

Abstract:

An algorithm using the differential transformation which is convenient for finding numerical solutions to initial value problems for functional differential equations is proposed in this paper. We focus on retarded equations with delays which in general are functions of the independent variable. The delayed differential equation is turned into an ordinary differential equation using the method of steps. The ordinary differential equation is transformed into a recurrence relation in one variable using the differential transformation. Approximate solution has the form of a Taylor polynomial whose coefficients are determined by solving the recurrence relation. Practical implementation of the presented algorithm is demonstrated in an example of the initial value problem for a differential equation with nonlinear nonconstant delay. A two-dimensional neutral system of higher complexity with constant, nonconstant, and proportional delays has been chosen to show numerical performance of the algorithm. Results are compared against Matlab function DDENSD.

APA, Harvard, Vancouver, ISO, and other styles

3

Methfessel, C. "On the zeros of recurrence sequences with non-constant coefficients." Archiv der Mathematik 74, no. 3 (2000): 201–6. http://dx.doi.org/10.1007/s000130050431.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Bertók, Csanád, Lajos Hajdu, István Pink, and Zsolt Rábai. "Linear combinations of prime powers in binary recurrence sequences." International Journal of Number Theory 13, no. 02 (2017): 261–71. http://dx.doi.org/10.1142/s1793042117500166.

Full text

Abstract:

We give finiteness results concerning terms of linear recurrence sequences having a representation as a linear combination, with fixed coefficients, of powers of fixed primes. On one hand, under certain conditions, we give effective bounds for the terms of binary recurrence sequences with such a representation. On the other hand, in the case of some special binary recurrence sequences, all terms having a representation as sums of powers of [Formula: see text] and [Formula: see text] are explicitly determined.

APA, Harvard, Vancouver, ISO, and other styles

5

Natalini, Pierpaolo, and Paolo Ricci. "Higher order bell polynomials and the relevant integer sequences." Applicable Analysis and Discrete Mathematics 11, no. 2 (2017): 327–39. http://dx.doi.org/10.2298/aadm1702327n.

Full text

Abstract:

The recurrence relation for the coefficients of higher order Bell polynomials, i.e. of the Bell polynomials relevant to nth derivative of a multiple composite function, is proved. Therefore, starting from this recurrence relation and by using the computer algebra program Mathematica?, some tables for complete higher order Bell polynomials and the relevant numbers are derived.

APA, Harvard, Vancouver, ISO, and other styles

6

Hubálovská, Marie, Štěpán Hubálovský, and Eva Trojovská. "On Homogeneous Combinations of Linear Recurrence Sequences." Mathematics 8, no. 12 (2020): 2152. http://dx.doi.org/10.3390/math8122152.

Full text

Abstract:

Let (Fn)n≥0 be the Fibonacci sequence given by Fn+2=Fn+1+Fn, for n≥0, where F0=0 and F1=1. There are several interesting identities involving this sequence such as Fn2+Fn+12=F2n+1, for all n≥0. In 2012, Chaves, Marques and Togbé proved that if (Gm)m is a linear recurrence sequence (under weak assumptions) and Gn+1s+⋯+Gn+ℓs∈(Gm)m, for infinitely many positive integers n, then s is bounded by an effectively computable constant depending only on ł and the parameters of (Gm)m. In this paper, we shall prove that if P(x1,…,xℓ) is an integer homogeneous s-degree polynomial (under weak hypotheses) and if P(Gn+1,…,Gn+ℓ)∈(Gm)m for infinitely many positive integers n, then s is bounded by an effectively computable constant depending only on ℓ, the parameters of (Gm)m and the coefficients of P.

APA, Harvard, Vancouver, ISO, and other styles

7

Branquinho, Amílcar, Juan Garca-Ardila, and Francisco Marcellán. "Ratio asymptotics for biorthogonal matrix polynomials with unbounded recurrence coefficients." Applicable Analysis and Discrete Mathematics, no. 00 (2020): 51. http://dx.doi.org/10.2298/aadm190225051b.

Full text

Abstract:

In this paper we study matrix biorthogonal polynomials sequences that satisfy a nonsymmetric three term recurrence relation with unbounded matrix coefficients. The outer ratio asymptotics for this family of matrix biorthogonal polynomials is derived under quite general assumptions. Some illustrative examples are considered.

APA, Harvard, Vancouver, ISO, and other styles

8

Dominici, Diego. "Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis." Bulletin of Mathematical Sciences 10, no. 02 (2020): 2050003. http://dx.doi.org/10.1142/s1664360720500034.

Full text

Abstract:

We study the three-term recurrence coefficients [Formula: see text] of polynomial sequences orthogonal with respect to a perturbed linear functional depending on a variable [Formula: see text] We obtain power series expansions in [Formula: see text] and asymptotic expansions as [Formula: see text] We use our results to settle some conjectures proposed by Walter Van Assche and collaborators.

APA, Harvard, Vancouver, ISO, and other styles

9

ANDRICA, DORIN, and OVIDIU BAGDASAR. "On some results concerning the polygonal polynomials." Carpathian Journal of Mathematics 35, no. 1 (2019): 01–12. http://dx.doi.org/10.37193/cjm.2019.01.01.

Full text

Abstract:

In this paper we define the nth polygonal polynomial and we investigate recurrence relations and exact integral formulae for the coefficients of Pn and for those of the Mahonianpolynomials. We also explore numerical properties of these coefficients, unraveling new meanings for old sequences and generating novel entries to the Online Encyclopedia of Integer Sequences (OEIS). Some open questions are also formulated.

APA, Harvard, Vancouver, ISO, and other styles

10

Dubickas, Artūras. "Intervals without primes near elements of linear recurrence sequences." International Journal of Number Theory 14, no. 02 (2018): 567–79. http://dx.doi.org/10.1142/s1793042118500355.

Full text

Abstract:

Let [Formula: see text] be an unbounded sequence of integers satisfying a linear recurrence relation with integer coefficients. We show that for any [Formula: see text] there exist infinitely many [Formula: see text] for which [Formula: see text] consecutive integers [Formula: see text] are all divisible by certain primes. Moreover, if the sequence of integers [Formula: see text] satisfying a linear recurrence relation is unbounded and non-degenerate then for some constant [Formula: see text] the intervals [Formula: see text] do not contain prime numbers for infinitely many [Formula: see text]. Applying this argument to sequences of integer parts of powers of Pisot and Salem numbers [Formula: see text] we derive a similar result for those sequences as well which implies, for instance, that the shifted integer parts [Formula: see text], where [Formula: see text] and [Formula: see text] runs through some infinite arithmetic progression of positive integers, are all composite.

APA, Harvard, Vancouver, ISO, and other styles

More sources

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!