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Generating function

In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.

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Definition

Types

Ordinary generating functions

Applications

Citations

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Generating function

Nodes151
Edges150
Triples166
Avg. degree1.99
Density0.013245
Components1

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Generating function

Top relations

related to Citations · 59
Generating function → Academic Press, Addison-Wesley, Aigner, American Mathematical Society, Analytic Combinatorics, Cambridge University Press, Chapter, Combinatorial Enumeration, Concrete Mathematics, Course, David, Donald, Doubilet, Dover Publications, Enumeration, Finite Operator Calculus, Flajolet, Generating Functions, Generatingfunctionology, Gian-Carlo
related to External links · 14
Generating function → Coin Change, Ed Pegg Jr, EMS Press, Encyclopedia, Functions, Generating, Generating Functions, Introduction To Ordinary Generating, Mathematics, Mike Zabrocki, Power Indices, Statistics, Wolfram Demonstrations Project, York University
has application · 8
Generating function → Evaluate, Explore, Fibonacci, Find, Generating, Prove, Rook, Solve
related to Generating functions prove congruences · 8
Generating function → Euler, For, Generating Functions, If, J-fractions, Lando's Lectures, One, We
related to Convergence · 6
Generating function → However, Indeed, One, These, Thus, Unlike
related to Dirichlet series generating functions (DGFs) · 6
Generating function → Bell, BG, DG, Euler, Formal Dirichlet, The Dirichlet
related to Polynomial sequence generating functions · 6
Generating function → Appell, Examples, See, Sheffer, The, Thus
related to Rational functions · 6
Generating function → Binet's, Conversely, Fibonacci, The, This, We
related to history · 5
Generating function → Abraham, Generating, George Pólya, Mathematics, Moivre
related to Tables of special generating functions · 5
Generating function → An, Concrete Mathematics, Other, Section, Wilf's Generatingfunctionology

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Important terminology

generating function displaystyle sum functions frac sequence infty series ordinary sequences left right numbers power form example coefficients binom begin

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Generating functionis arepresentation of an infinite sequence of numbers as the coefficients of a formal power series0.90text
Generating functionis adevice somewhat similar to a bag0.90text
Generating functionis aclothesline on which we hang up a sequence of numbers for display0.90text
Generating functionis ageometric series0.90text
tan zinstance offunctions with infinitely many singularities0.80text
sec zinstance offunctions with infinitely many singularities0.80text
and Γinstance offunctions with infinitely many singularities0.80text
qinstance ofwhen these sequences do not implicitly depend on an auxiliary parameter0.80text
xinstance ofwhen these sequences do not implicitly depend on an auxiliary parameter0.80text
or R as in the examples contained in the table below.ExamplesThe next table provides examples of closed-form formulas for the component sequences found computationallyinstance ofwhen these sequences do not implicitly depend on an auxiliary parameter0.80text
or R as in the examples contained in the table belowinstance ofwhen these sequences do not implicitly depend on an auxiliary parameter0.80text
Generating functionhas applicationGenerating0.60section

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