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Holonomic function: Measurement, Holonomic functions and sequences in one variable & Algorithms and software

In mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension condition in terms of D-modules theory. More precisely, a holonomic function is an element of a…

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Holonomic function topic overview

The analysis highlights Measurement, Holonomic functions and sequences in one variable and Algorithms and software as prominent areas in the source structure around Holonomic function.

Related topics
46
Source areas
3
Connected nodes
49
Extracted relationships
84
Concept neighborhoods
26
Bridge connections
49

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Holonomic functions and sequences in one variable · 36 topics
Overview · 7 topics
Algorithms and software · 3 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Holonomic functions and sequences in one variable

Algorithms and software

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Holonomic function connects Entity context

The extracted context around Holonomic function shows recurring relationship patterns in the source. For example, Holonomic function → Algorithmic Manipulations, Algorithms, Analytic Combinatorics, Applied Mathematics, Asymptotic Estimates, Bruno, Cambridge University Press, Christian, Combinatorics, Computation, Computational, D-Finite Functions, Doron, Electronic Journal, Enumerative Combinatorics, Flajolet, Generating Functions, Gerhold, Irreducible, ISBN Another extracted example is Holonomic function → Ai, Airy, Bessel, Bi, Examples. Use these groups to spot repeated connection types before inspecting the individual relationships.

Holonomic function

Top relations

related to References · 61
Holonomic function → Algorithmic Manipulations, Algorithms, Analytic Combinatorics, Applied Mathematics, Asymptotic Estimates, Bruno, Cambridge University Press, Christian, Combinatorics, Computation, Computational, D-Finite Functions, Doron, Electronic Journal, Enumerative Combinatorics, Flajolet, Generating Functions, Gerhold, Irreducible, ISBN
related to Examples of holonomic functions and sequences · 5
Holonomic function → Ai, Airy, Bessel, Bi, Examples
see also · 5
Holonomic function → Archived, Dynamic Dictionary, Mathematical, Taylor, Wayback Machine
related to Closure properties · 4
Holonomic function → Holonomic, If, In, They
related to Algorithms and software · 3
Holonomic function → Holonomic, In, Moreover
is a · 2
Holonomic function → element of a holonomic module of smooth functions, smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension…
related to Examples of nonholonomic functions and sequences · 1
Holonomic function → Examples

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

holonomic functions displaystyle function sequence sequences also operator called coefficients annihilating examples mathbb series closure properties polynomials isbn form include

Holonomic function relationships Subject–Predicate–Object triples

TTTA extracted 84 structured relationships around Holonomic function. Examples in this analysis include Holonomic function → is a → smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension… and Holonomic function → is a → element of a holonomic module of smooth functions. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Holonomic functionis asmooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension…0.90text
Holonomic functionis aelement of a holonomic module of smooth functions0.90text
equality testinginstance ofand the closure properties allow carrying out operations0.80text
summationinstance ofand the closure properties allow carrying out operations0.80text
integration in an algorithmic fashioninstance ofand the closure properties allow carrying out operations0.80text
Holonomic functionrelated to Algorithms and softwareHolonomic0.60section
Holonomic functionrelated to Algorithms and softwareIn0.60section
Holonomic functionrelated to Algorithms and softwareMoreover0.60section
Holonomic functionrelated to Closure propertiesHolonomic0.60section
Holonomic functionrelated to Closure propertiesIn0.60section
Holonomic functionrelated to Closure propertiesThey0.60section
Holonomic functionrelated to Closure propertiesIf0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Holonomic function bring nearby vocabulary together. In this analysis, examples include Functions, Function and Holonomic. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Holonomic function
    • Functions
    • Function
    • Holonomic
    • Displaystyle
    • Sequence
    • Sequences
    • Coefficients
    • Also
    • Closure
    • Properties
    • Examples
    • Smooth
  • holonomic function
    • Functions
    • Function
    • Holonomic
    • Displaystyle
    • Sequence
    • Sequences
    • Series
    • Coefficients
    • Also
    • Closure
    • Properties
    • Examples
  • function of several variables
    • Several
    • Variables
    • Holonomic
    • Coefficients
    • Homogeneous
    • Polynomial
    • Satisfies
    • Smooth
    • Suitable
    • Differential
    • Expansion
    • Linear
  • linear homogeneous differential equations
    • Polynomial
    • Satisfies
    • Homogeneous
    • Linear
    • Recurrence
    • Coefficients
    • Smooth
    • Suitable
    • Variables
    • Differential
    • Mathematics
    • Several
  • holonomic module
    • Functions
    • Function
    • Displaystyle
    • Sequence
    • Sequences
    • Coefficients
    • Also
    • Closure
    • Properties
    • Examples
    • Polynomials
    • Include
  • differential operator
    • Order
    • Coefficients
    • Homogeneous
    • Polynomial
    • Satisfies
    • Smooth
    • Suitable
    • Variables
    • Expansion
    • Linear
    • Mathematics
    • Several
  • generating functions
    • Holonomic
    • Sequences
    • Displaystyle
    • Examples
    • Closure
    • Include
    • Properties
    • Also
    • Recurrence
    • Special
    • Sequence
    • Expansion
  • algebraic functions
    • Holonomic
    • Sequences
    • Displaystyle
    • Examples
    • Closure
    • Include
    • Properties
    • Also
    • Recurrence
    • Special
    • Sequence
    • Expansion

Connections between topic areas Semantic bridges

For Holonomic function, one of the stronger structural bridges in this analysis connects Holonomic function with Holonomic functions and sequences in one variable. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Holonomic functionHolonomic functions and sequences in one variable · splits 13 ⟂ 37
Holonomic functionOverview · splits 42 ⟂ 8
Holonomic functionAlgorithms and software · splits 46 ⟂ 4

Map overview Semantic statistics

Holonomic function

Nodes50
Edges49
Triples84
Avg. degree1.96
Density0.04
Components1

Source & methodology

TTTA analyzes the structure around Holonomic function to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Measurement, Holonomic functions and sequences in one variable & Algorithms and software, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Holonomic function · EN edition · Analysis: TopicsToTalkAbout

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