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Multiplication theorem: Characters & Products

In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name. The various relations all stem from the same underlying principle; that is, the relation for one special function can be…

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Multiplication theorem topic overview

The analysis highlights Characters and Products as prominent areas in the source structure around Multiplication theorem.

Related topics
44
Source areas
11
Connected nodes
55
Extracted relationships
42
Concept neighborhoods
32
Bridge connections
55

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.

Bernoulli map · 14 topics
Finite characteristic · 5 topics
Periodic zeta function · 5 topics
Polygamma function, harmonic numbers · 4 topics
Gamma function–Legendre formula · 3 topics
Hurwitz zeta function · 3 topics
Overview · 3 topics
Bernoulli polynomials · 2 topics
Characteristic zero · 2 topics
Polylogarithm · 2 topics
Kummer's function · 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

Finite characteristic

Gamma function–Legendre formula

Polygamma function, harmonic numbers

Hurwitz zeta function

Periodic zeta function

Polylogarithm

Kummer's function

Bernoulli polynomials

Bernoulli map

Characteristic zero

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 Multiplication theorem connects Entity context

The extracted context around Multiplication theorem shows recurring relationship patterns in the source. For example, Multiplication theorem → Addition, Dover, Formulas, Graphs, Handbook, Irene, Mathematical Functions, Mathematical Tables, Mathematics, Milton Abramowitz, Multiplication, Multiplication Theorems, National Academy, New York, On, Proceedings, Sciences, Special Functions, Stegun, Truesdell Another extracted example is Multiplication theorem → Chowla, For, In, Selberg, The. Use these groups to spot repeated connection types before inspecting the individual relationships.

Multiplication theorem

Top relations

related to References · 20
Multiplication theorem → Addition, Dover, Formulas, Graphs, Handbook, Irene, Mathematical Functions, Mathematical Tables, Mathematics, Milton Abramowitz, Multiplication, Multiplication Theorems, National Academy, New York, On, Proceedings, Sciences, Special Functions, Stegun, Truesdell
related to Finite characteristic · 5
Multiplication theorem → Chowla, For, In, Selberg, The
related to Bernoulli polynomials · 4
Multiplication theorem → Bernoulli, Euler, For, Joseph Ludwig Raabe
related to Characteristic zero · 4
Multiplication theorem → Bessel, Examples, Such, The
related to Gamma function–Legendre formula · 4
Multiplication theorem → Adrien-Marie Legendre, It, Legendre, The
related to Hurwitz zeta function · 3
Multiplication theorem → Riemann, The Hurwitz, This
is a · 1
Multiplication theorem → certain type of identity obeyed by many special functions related to the gamma function
related to Polygamma function, harmonic numbers · 1
Multiplication theorem → The

Important terminology

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

Important terminology

function multiplication theorem formula gamma bernoulli case special duplication thus zeta displaystyle functions one identity periodic relation finite polynomials polylogarithm

Multiplication theorem relationships Subject–Predicate–Object triples

TTTA extracted 42 structured relationships around Multiplication theorem. Examples in this analysis include Multiplication theorem → is a → certain type of identity obeyed by many special functions related to the gamma function and Multiplication theorem → related to Bernoulli polynomials → For. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Multiplication theoremis acertain type of identity obeyed by many special functions related to the gamma function0.90text
Multiplication theoremrelated to Bernoulli polynomialsFor0.60section
Multiplication theoremrelated to Bernoulli polynomialsBernoulli0.60section
Multiplication theoremrelated to Bernoulli polynomialsJoseph Ludwig Raabe0.60section
Multiplication theoremrelated to Bernoulli polynomialsEuler0.60section
Multiplication theoremrelated to Characteristic zeroThe0.60section
Multiplication theoremrelated to Characteristic zeroExamples0.60section
Multiplication theoremrelated to Characteristic zeroBessel0.60section
Multiplication theoremrelated to Characteristic zeroSuch0.60section
Multiplication theoremrelated to Finite characteristicThe0.60section
Multiplication theoremrelated to Finite characteristicIn0.60section
Multiplication theoremrelated to Finite characteristicFor0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Multiplication theorem bring nearby vocabulary together. In this analysis, examples include Theorem, Formula and Zeta. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Multiplication theorem
    • Theorem
    • Formula
    • Zeta
    • Special
    • Thus
    • Case
    • Bernoulli
    • Hurwitz
    • May
    • Multiplicative
    • Obeys
    • Polynomials
  • multiplication theorem
    • Theorem
    • Formula
    • Zeta
    • Special
    • Multiplicative
    • Obeys
    • Thus
    • Case
    • Bernoulli
    • Hurwitz
    • May
    • Polynomials
  • special functions
    • Case
    • Mathematics
    • Related
    • Special
    • Gamma
    • Identity
    • Multiplication
    • Given
    • May
    • Polynomials
    • Theorem
    • Bernoulli
  • gamma function
    • Multiplication
    • Theorem
    • Formula
    • Thus
    • Zeta
    • Function
    • Gamma
    • Identity
    • Duplication
    • Periodic
    • Hurwitz
    • Numbers
  • finite field
    • Zero
    • Number
    • Terms
    • Relation
    • Gamma
    • Theorem
    • Polygamma
    • Related
    • Relations
    • Given
    • Hurwitz
    • Identity
  • chowla–selberg formula
    • Duplication
    • Gamma
    • Theorem
    • Function
    • Multiplication
    • Periodic
    • Zeta
    • Polygamma
    • Hurwitz
    • Numbers
    • Polylogarithm
    • Identities
  • complex multiplication
    • Theorem
    • Formula
    • Zeta
    • Special
    • Thus
    • Case
    • Bernoulli
    • Hurwitz
    • May
    • Multiplicative
    • Obeys
    • Polynomials
  • polygamma function
    • Multiplication
    • Theorem
    • Thus
    • Zeta
    • Formula
    • Gamma
    • Duplication
    • Displaystyle
    • Periodic
    • Hurwitz
    • Numbers
    • Identities

Connections between topic areas Semantic bridges

For Multiplication theorem, one of the stronger structural bridges in this analysis connects Multiplication theorem with Bernoulli map. 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
Multiplication theorem — Bernoulli map · splits 41 ⟂ 15
Multiplication theorem — Finite characteristic · splits 50 ⟂ 6
Multiplication theorem — Periodic zeta function · splits 50 ⟂ 6
Multiplication theorem — Polygamma function, harmonic numbers · splits 51 ⟂ 5
Multiplication theorem — Overview · splits 52 ⟂ 4
Multiplication theorem — Gamma function–Legendre formula · splits 52 ⟂ 4
Multiplication theorem — Hurwitz zeta function · splits 52 ⟂ 4
Multiplication theorem — Polylogarithm · splits 53 ⟂ 3
Multiplication theorem — Bernoulli polynomials · splits 53 ⟂ 3
Multiplication theorem — Characteristic zero · splits 53 ⟂ 3

Map overview Semantic statistics

Multiplication theorem

Nodes56
Edges55
Triples42
Avg. degree1.96
Density0.035714
Components1

Source & methodology

TTTA analyzes the structure around Multiplication theorem to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Characters & Products, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Multiplication theorem · EN edition · Analysis: TopicsToTalkAbout

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