scholarly journals Recursive sequences and girard-waring identities with applications in sequence transformation

2020 ◽  
Vol 28 (2) ◽  
pp. 1049-1062
Author(s):  
Tian-Xiao He ◽  
◽  
Peter J.-S. Shiue ◽  
Zihan Nie ◽  
Minhao Chen ◽  
...  
Keyword(s):  
Recursive Sequences ◽  
Sequence Transformation

scholarly journals Identities for linear recursive sequences of order $ 2 $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tian-Xiao He ◽  
Peter J.-S. Shiue
Keyword(s):  
General Rule ◽  
Transformation Techniques ◽  
Polynomial Sequences ◽  
Recursive Sequences ◽  
Number Sequences ◽  
Sequence Transformation

<p style='text-indent:20px;'>We present here a general rule of construction of identities for recursive sequences by using sequence transformation techniques developed in [<xref ref-type="bibr" rid="b16">16</xref>]. Numerous identities are constructed, and many well known identities can be proved readily by using this unified rule. Various Catalan-like and Cassini-like identities are given for recursive number sequences and recursive polynomial sequences. Sets of identities for Diophantine quadruple are shown.</p>

scholarly journals Log-concavity of P-recursive sequences

2021 ◽  
Vol 107 ◽  
pp. 251-268
Author(s):  
Qing-hu Hou ◽  
Guojie Li
Keyword(s):  
Recursive Sequences

scholarly journals Polynomials and General Degree-Based Topological Indices of Generalized Sierpinski Networks

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chengmei Fan ◽  
M. Mobeen Munir ◽  
Zafar Hussain ◽  
Muhammad Athar ◽  
Jia-Bao Liu
Keyword(s):  
Complex Systems ◽  
Computer Science ◽  
Topological Indices ◽  
Fractal Nature ◽  
Similar Nature ◽  
Zagreb Index ◽  
Recursive Sequences ◽  
And Mathematics

Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems. In this article, we compute various connectivity polynomials such as M -polynomial, Zagreb polynomials, and forgotten polynomial of generalized Sierpinski networks S k n and recover some well-known degree-based topological indices from these. We also compute the most general Zagreb index known as α , β -Zagreb index and several other general indices of similar nature for this network. Our results are the natural generalizations of already available results for particular classes of such type of networks.

scholarly journals Convolution of second order linear recursive sequences II.

2017 ◽  
Vol 25 (2) ◽  
pp. 137-148
Author(s):  
Tamás Szakács
Keyword(s):  
Second Order ◽  
Characteristic Polynomials ◽  
Common Root ◽  
Order Linear ◽  
Recursive Sequences

Abstract We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.

Symmetric Recursive Sequences Mod M

1988 ◽  
pp. 17-28 ◽  
Author(s):  
Kenji Nagasaka ◽  
Shiro Ando
Keyword(s):  
Recursive Sequences

Introduction to Stochastic Processes

2019 ◽  
pp. 1-24
Author(s):  
Florence Merlevède ◽  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Dynamical Systems ◽  
Stochastic Processes ◽  
Gaussian Approximation ◽  
Partial Sums ◽  
Stationary Sequences ◽  
Linear Processes ◽  
Limiting Behavior ◽  
Additive Functionals ◽  
Moderate Deviations Principle ◽  
Recursive Sequences

We start by stating the need for a Gaussian approximation for dependent structures in the form of the central limit theorem (CLT) or of the functional CLT. To justify the need to quantify the dependence, we introduce illustrative examples: linear processes, functions of stationary sequences, recursive sequences, dynamical systems, additive functionals of Markov chains, and self-interactions. The limiting behavior of the associated partial sums can be handled with tools developed throughout the book. We also present basic notions for stationary sequences of random variables: various definitions and constructions, and definitions of ergodicity, projective decomposition, and spectral density. Special attention is given to dynamical systems, as many of our results also apply in this context. The chapter also surveys the basic theory of the convergence of stochastic processes in distribution, and introduces the reader to tightness, finite-dimensional convergence, and the need for maximal inequalities. It ends with the concepts of the moderate deviations principle and its functional form.

Sign in / Sign up

Export Citation Format

Share Document