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Polygamma function: Recurrence relation, Series representation & Integral representation

In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers C {\displaystyle \mathbb {C} } defined as the (m + 1)th derivative of the logarithm of the gamma function:

Language: English [EN]
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Polygamma function topic overview

The analysis highlights Recurrence relation, Series representation and Integral representation as prominent areas in the source structure around Polygamma function.

Related topics
33
Source areas
8
Connected nodes
41
Extracted relationships
7
Concept neighborhoods
25
Bridge connections
41

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.

Overview · 9 topics
Recurrence relation · 8 topics
Series representation · 5 topics
Inequalities · 3 topics
Integral representation · 3 topics
Taylor series · 3 topics
Asymptotic expansion · 1 topics
Multiplication theorem · 1 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

Integral representation

Recurrence relation

Multiplication theorem

Series representation

Taylor series

Asymptotic expansion

Inequalities

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 Polygamma function connects Entity context

The extracted context around Polygamma function shows recurring relationship patterns in the source. For example, Polygamma function → Hurwitz, Re, When Another extracted example is Polygamma function → Hurwitz, The, This. Use these groups to spot repeated connection types before inspecting the individual relationships.

Polygamma function

Top relations

related to Integral representation · 3
Polygamma function → Hurwitz, Re, When
related to Series representation · 3
Polygamma function → Hurwitz, The, This
see also · 1
Polygamma function → FactorialGamma

Important terminology

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

Important terminology

function polygamma displaystyle functions representation series gamma digamma mathbb theorem trigamma zeta strictly numbers order integral relation case positive psi

Polygamma function relationships Subject–Predicate–Object triples

TTTA extracted 7 structured relationships around Polygamma function. Examples in this analysis include Polygamma function → related to Integral representation → When and Polygamma function → related to Integral representation → Re. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Polygamma functionrelated to Integral representationWhen0.60section
Polygamma functionrelated to Integral representationRe0.60section
Polygamma functionrelated to Integral representationHurwitz0.60section
Polygamma functionrelated to Series representationThe0.60section
Polygamma functionrelated to Series representationThis0.60section
Polygamma functionrelated to Series representationHurwitz0.60section
Polygamma functionsee alsoFactorialGamma0.60section

Related concept clusters Concept neighborhoods

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

  • Polygamma function
    • Polygamma
    • Functions
    • Representation
    • Series
    • Displaystyle
    • Relation
    • Theorem
    • Gamma
    • Also
    • Holds
    • Thus
    • Hurwitz
  • polygamma function
    • Polygamma
    • Functions
    • Digamma
    • Representation
    • Series
    • Displaystyle
    • Relation
    • Trigamma
    • Theorem
    • Zeta
    • Gamma
    • Also
  • meromorphic function
    • Polygamma
    • Digamma
    • Representation
    • Displaystyle
    • Trigamma
    • Theorem
    • Zeta
    • Gamma
    • Series
    • Hurwitz
    • Taylor
    • Case
  • gamma function
    • Mathbb
    • Polygamma
    • Logarithm
    • Thus
    • Digamma
    • Representation
    • Numbers
    • Positive
    • Displaystyle
    • Strictly
    • Trigamma
    • Theorem
  • digamma function
    • Polygamma
    • Digamma
    • Function
    • Representation
    • Integral
    • Displaystyle
    • Gamma
    • Trigamma
    • Theorem
    • Zeta
    • Series
    • Holds
  • trigamma function
    • Polygamma
    • Digamma
    • Representation
    • Displaystyle
    • Trigamma
    • Theorem
    • Zeta
    • Gamma
    • Inequality
    • Series
    • Case
    • Hurwitz
  • hurwitz zeta function
    • Hurwitz
    • Zeta
    • Taylor
    • Relation
    • Polygamma
    • Series
    • Used
    • Digamma
    • Representation
    • Multiplication
    • Displaystyle
    • Order
  • n {\displaystyle \mathbb {n} }
    • Numbers
    • Mathbb
    • Strictly
    • Gamma
    • Positive
    • Psi
    • Recurrence
    • Relation
    • Monotonic
    • Polygamma
    • Function
    • Functions

Connections between topic areas Semantic bridges

For Polygamma function, one of the stronger structural bridges in this analysis connects Polygamma function with Overview. 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
Polygamma functionOverview · splits 32 ⟂ 10
Polygamma functionRecurrence relation · splits 33 ⟂ 9
Polygamma functionSeries representation · splits 36 ⟂ 6
Polygamma functionIntegral representation · splits 38 ⟂ 4
Polygamma functionTaylor series · splits 38 ⟂ 4
Polygamma functionInequalities · splits 38 ⟂ 4

Map overview Semantic statistics

Polygamma function

Nodes42
Edges41
Triples7
Avg. degree1.95
Density0.047619
Components1

Source & methodology

TTTA analyzes the structure around Polygamma function to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Recurrence relation, Series representation & Integral representation, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

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

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