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In mathematics, a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating function enumerating another. These transformations typically involve integral formulas applied to a sequence generating function (see integral transformations) or weighted sums over the higher-order derivatives of these functions (see derivative transformations).

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rdfs:label	Generating function transformation (en)
rdfs:comment	In mathematics, a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating function enumerating another. These transformations typically involve integral formulas applied to a sequence generating function (see integral transformations) or weighted sums over the higher-order derivatives of these functions (see derivative transformations). (en)
dcterms:subject	Generating functions
Wikipage page ID	53098313 (xsd:integer)
Wikipage revision ID	1122145408 (xsd:integer)
Link from a Wikipage to another Wikipage	Bell polynomials Root of unity Bernoulli number Bessel function Generating functions Riemann zeta function Pochhammer symbol Continued fraction Generating function transformation Function composition Gamma function Generating function Geometric series Golden ratio Möbius inversion formula Constant-recursive sequence Legendre polynomials Faulhaber's formula Faà di Bruno's formula Lerch zeta function Stirling number Trilogarithm Lambert series Alternating factorial Euler number Fibonacci number Formal power series Fractional calculus Barnes G-function Hankel contour Legendre chi function Harmonic number Inverse tangent Bailey–Borwein–Plouffe formula Hurwitz zeta function Laguerre polynomials Laplace transform Laurent series Binomial transform Dilogarithm Dirichlet eta function Double factorial Polygamma function Polylogarithm Imaginary unit Incomplete gamma function Natural logarithm Reciprocal gamma function Sequence Eulerian number Exponential integral Factorial List of zeta functions Pochhammer k-symbol Stirling numbers of the second kind Stirling numbers of the first kind Series multisection Stirling transform Bell polynomial Newton series Dirichlet generating function Derangements Stirling number of the second kind
Link from a Wikipage to an external page	http://plouffe.fr/simon/math/AdvancedComb.pdf https://archive.org/details/combinatorialide00john%7Curl-access=registration%7Cdate=1968%7Cpublisher=Wiley https://youtube.com/watch%3Fv=4AuV93LOPcE https://cs.uwaterloo.ca/journals/JIS/VOL20/Schmidt/schmidt14.html
sameAs	Generating function transformation Generating function transformation Generating function transformation
dbp:wikiPageUsesTemplate	dbt:About dbt:Cite_arXiv dbt:Cite_book dbt:Cite_journal dbt:Expand_section dbt:Main dbt:Reflist
has abstract	In mathematics, a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating function enumerating another. These transformations typically involve integral formulas applied to a sequence generating function (see integral transformations) or weighted sums over the higher-order derivatives of these functions (see derivative transformations). Given a sequence, , the ordinary generating function (OGF) of the sequence, denoted , and the exponential generating function (EGF) of the sequence, denoted , are defined by the formal power series In this article, we use the convention that the ordinary (exponential) generating function for a sequence is denoted by the uppercase function / for some fixed or formal when the context of this notation is clear. Additionally, we use the bracket notation for coefficient extraction from the Concrete Mathematics reference which is given by .The main article gives examples of generating functions for many sequences. Other examples of generating function variants include Dirichlet generating functions (DGFs), Lambert series, and Newton series. In this article we focus on transformations of generating functions in mathematics and keep a running list of useful transformations and transformation formulas. (en)
prov:wasDerivedFrom	wikipedia-en:Generating_function_transformation?oldid=1122145408&ns=0
page length (characters) of wiki page	63378 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Generating_function_transformation
is Link from a Wikipage to another Wikipage of	Bell polynomials Generating function transformation Generating function Z-transform Dirichlet series Dirichlet series inversion Hadamard product (series) Redheffer matrix Polylogarithm Stirling numbers of the first kind Series multisection Stirling transform
is Wikipage redirect of	Hadamard product (series)
is foaf:primaryTopic of	wikipedia-en:Generating_function_transformation

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