Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

382
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
382
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

297
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
297
Detection of Gross Error: The Q Test01:00

Detection of Gross Error: The Q Test

6.4K
When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
6.4K
Convergence of Fourier Series01:21

Convergence of Fourier Series

198
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
198
Determination of Pi Terms01:15

Determination of Pi Terms

337
The Buckingham Pi theorem is a valuable method in dimensional analysis, reducing complex relationships between variables into dimensionless terms. Relevant variables in analyzing the lift force on an airplane wing include lift force, air density, wing area, aircraft velocity, and air viscosity. Expressing each variable in terms of fundamental dimensions — mass, length, and time — provides a consistent foundation for constructing these dimensionless terms.
The theorem indicates that...
337
Cochran's Q Test01:17

Cochran's Q Test

524
Cochran's Q Test is a nonparametric statistical test used to determine if there are potential differences in the outcomes of three or more related groups on a binary (yes/no) or dichotomous outcome. It is essentially an extension of the McNemar Test, which is limited to two related samples - Cochran's Q test can handle three or more related samples, making it more versatile in scenarios where subjects are measured under multiple conditions. The test statistic follows a Chi-Square...
524

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Large subsets of  <math></math> without arithmetic progressions.

Designs, codes, and cryptography·2023
Same author

Analysis of carries in signed digit expansions.

Monatshefte fur Mathematik·2020
Same author

Asymptotic Analysis of Regular Sequences.

Algorithmica·2020
See all related articles

Related Experiment Video

Updated: Sep 1, 2025

Author Spotlight: AQRNA-seq Role in Mapping Small RNAs and Unraveling Protein Translation Mechanisms
05:12

Author Spotlight: AQRNA-seq Role in Mapping Small RNAs and Unraveling Protein Translation Mechanisms

Published on: February 2, 2024

883

Asymptotic Analysis of q-Recursive Sequences.

Clemens Heuberger1, Daniel Krenn2, Gabriel F Lipnik3

  • 1Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria.

Algorithmica
|August 17, 2022
PubMed
Summary
This summary is machine-generated.

This study analyzes q-recursive sequences, demonstrating they are q-regular. The research provides a method to compute their q-linear representation and details their asymptotic behavior, including precise formulas for specific sequences.

Keywords:
Asymptotic analysisDigital functionDirichlet seriesPascal’s triangleRecurrence relationRegular sequenceStern’s diatomic sequenceSummatory functionThue–Morse sequence

More Related Videos

A Quantitative Fitness Analysis Workflow
11:39

A Quantitative Fitness Analysis Workflow

Published on: August 13, 2012

14.6K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.7K

Related Experiment Videos

Last Updated: Sep 1, 2025

Author Spotlight: AQRNA-seq Role in Mapping Small RNAs and Unraveling Protein Translation Mechanisms
05:12

Author Spotlight: AQRNA-seq Role in Mapping Small RNAs and Unraveling Protein Translation Mechanisms

Published on: February 2, 2024

883
A Quantitative Fitness Analysis Workflow
11:39

A Quantitative Fitness Analysis Workflow

Published on: August 13, 2012

14.6K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.7K

Area of Science:

  • Number Theory
  • Discrete Mathematics
  • Theoretical Computer Science

Background:

  • q-recursive sequences are defined by recurrence relations based on indices modulo powers of q.
  • Understanding the asymptotic behavior of these sequences is crucial for various mathematical and computational applications.

Purpose of the Study:

  • To study q-recursive sequences and analyze the asymptotic behavior of their summatory functions.
  • To establish the connection between q-recursive and q-regular sequences.
  • To derive precise asymptotic formulas for specific mathematical sequences.

Main Methods:

  • Defining q-recursive sequences using recurrence relations modulo powers of q.
  • Proving that every q-recursive sequence is q-regular (Allouche & Shallit).
  • Utilizing a general result on the asymptotic analysis of q-regular sequences.

Main Results:

  • Every q-recursive sequence is shown to be q-regular.
  • A q-linear representation of q-recursive sequences can be easily computed.
  • Detailed asymptotic results for q-recursive sequences are derived.
  • Precise formulas without error terms are obtained for Stern's diatomic sequence and the number of non-zero elements in generalized Pascal's triangles.

Conclusions:

  • The study establishes q-recursive sequences as a subset of q-regular sequences.
  • The methods provide a framework for analyzing the asymptotic behavior of a broad class of sequences.
  • The findings offer exact results for specific, notable sequences in number theory and combinatorics.