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Title: Generating Function -- from Wolfram MathWorld

Open Graph Title: Generating Function -- from Wolfram MathWorld

X Title: Generating Function -- from Wolfram MathWorld

Description: A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command GeneratingFunction[expr, n, x] gives the generating function in the variable x for the sequence whose nth term is expr. Given a sequence of terms, FindGeneratingFunction[{a1, a2, ...}, x] attempts to find a simple generating function in x whose nth coefficient is a_n. Given a generating function, the analytic expression for...

Open Graph Description: A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command GeneratingFunction[expr, n, x] gives the generating function in the variable x for the sequence whose nth term is expr. Given a sequence of terms, FindGeneratingFunction[{a1, a2, ...}, x] attempts to find a simple generating function in x whose nth coefficient is a_n. Given a generating function, the analytic expression for...

X Description: A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command GeneratingFunction[expr, n, x] gives the generating function in the variable x for the sequence whose nth term is expr. Given a sequence of terms, FindGeneratingFunction[{a1, a2, ...}, x] attempts to find a simple generating function in x whose nth coefficient is a_n. Given a generating function, the analytic expression for...

Opengraph URL: https://mathworld.wolfram.com/GeneratingFunction.html

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direct link

Domain: mathworld.wolfram.com

DC.TitleGenerating Function
DC.CreatorWeisstein, Eric W.
DC.DescriptionA generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command GeneratingFunction[expr, n, x] gives the generating function in the variable x for the sequence whose nth term is expr. Given a sequence of terms, FindGeneratingFunction[{a1, a2, ...}, x] attempts to find a simple generating function in x whose nth coefficient is a_n. Given a generating function, the analytic expression for...
DC.Date.Modified2008-11-15
DC.Subject05A15
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/GeneratingFunction.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2008-11-15
og:imagehttps://mathworld.wolfram.com/images/socialmedia/share/ogimage_GeneratingFunction.png
og:typewebsite
twitter:cardsummary_large_image
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Generating Functionshttps://mathworld.wolfram.com/topics/GeneratingFunctions.html
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formal power serieshttps://mathworld.wolfram.com/FormalPowerSeries.html
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sequencehttps://mathworld.wolfram.com/Sequence.html
Wolfram Languagehttp://www.wolfram.com/language/
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FindGeneratingFunctionhttp://reference.wolfram.com/language/ref/FindGeneratingFunction.html
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Finite Operator Calculushttp://www.amazon.com/exec/obidos/ASIN/B00072GPAU/ref=nosim/ericstreasuretro
Concrete Mathematics: A Foundation for Computer Science, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/0201558025/ref=nosim/ericstreasuretro
Graphical Enumeration.http://www.amazon.com/exec/obidos/ASIN/0123242452/ref=nosim/ericstreasuretro
Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed.http://www.amazon.com/exec/obidos/ASIN/0821820230/ref=nosim/ericstreasuretro
Lectures on Generating Functions.http://www.amazon.com/exec/obidos/ASIN/0821834819/ref=nosim/ericstreasuretro
Combinatorial Identities.http://www.amazon.com/exec/obidos/ASIN/0882758292/ref=nosim/ericstreasuretro
An Introduction to Combinatorial Analysis.http://www.amazon.com/exec/obidos/ASIN/0691023654/ref=nosim/ericstreasuretro
Discrete Mathematics and Its Applications, 4th ed.http://www.amazon.com/exec/obidos/ASIN/0072899050/ref=nosim/ericstreasuretro
The Encyclopedia of Integer Sequences.http://www.amazon.com/exec/obidos/ASIN/0125586302/ref=nosim/ericstreasuretro
Enumerative Combinatorics, Vol. 1.http://www.amazon.com/exec/obidos/ASIN/0521553091/ref=nosim/ericstreasuretro
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