Examples of generating functions
label: دالة مولدة @ar
label: Genererande funktion @sv
label: Funció generatriu @ca
label: 생성함수 (수학) @ko
label: Генератриса @uk
label: Производящая функция последовательности @ru
label: 母函数 @zh
label: Funzione generatrice @it
label: Fungsi pembangkit @in
label: Erzeugende Funktion @de
label: Funkcja tworząca @pl
label: Voortbrengende functie @nl
label: Generating function
label: Vytvořující funkce (posloupnost) @cs
label: Função geradora @pt
label: Série génératrice @fr
label: 母関数 @ja
label: Función generadora @es
subject: Category:1730 introductions
subject: Category:Abraham de Moivre
subject: Category:Generating functions
author: George Pólya
author: Herbert Wilf
id: p/g043900
source: Mathematics and plausible reasoning
source: Generatingfunctionology
text: A generating function is a clothesline on which we hang up a sequence of numbers for display.
text: A generating function is a device somewhat similar to a bag. Instead of carrying many little objects detachedly, which could be embarrassing, we put them all in a bag, and then we have only one object to carry, the bag.
name: Theorem: congruences for series generated by expansions of continued fractions
description: formal power series with coefficients that encode information about a sequence
description: série formelle dont les coefficients codent une suite @fr
description: szereg formalny, w którym współczynniki przy poszczególnych potęgach odpowiadają elementom danego ciągu indeksowanego liczbami naturalnymi @pl
description: Fonksiyon @tr
description: Art von formaler Potenzreihe @de
description: formala potencoserio kies koeficientoj reprezentas iun nombrovicon @eo
description: 조합론의 개념 @ko
description: serie formal de potencias con coeficientes que codifican información sobre unha secuencia @gl
description: 形式冪級數，其系數隱含某數列的資訊 @zh
description: tipo di serie formale di potenze @it
description: یک سری توانی در ریاضیات @fa
wiki page external link: http://projecteuclid.org/euclid.bsmsp/1200514223
wiki page external link: https://books.google.com/books%3Fid=pPEJcu93dzAC
wiki page external link: http://www.math.upenn.edu/%7Ewilf/DownldGF.html
wiki page external link: https://books.google.com/books%3Fid=A6_4AwAAQBAJ
wiki page external link: http://garsia.math.yorku.ca/~zabrocki/MMM1/MMM1Intro2OGFs.pdf
wiki page external link: http://demonstrations.wolfram.com/GeneratingFunctions/
wiki page external link: https://oeis.org/search%3Fq=1%2C1%2C2%2C2%2C3%2C5%2C5%2C7%2C10%2C15%2C15&sort=&language=&go=Search
wiki page external link: http://www.math.upenn.edu/~wilf/DownldGF.html
wiki page external link: https://www.risc.jku.at/research/combinat/software/
wiki page external link: http://www.cut-the-knot.org/ctk/GeneratingFunctions.shtml
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Function_(mathematics)
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Generalized_hypergeometric_function
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Euler–Maclaurin_formula
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Cauchy_product
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Multiset_coefficient
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Moment-generating_function
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Ed_Pegg_Jr.
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Laplace
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Divisor_function
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Dirichlet_character
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Order_of_accuracy
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Difference_polynomials
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Q-Pochhammer_symbol
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Lambert_series
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Codomain
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Bell_series
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Radius_of_convergence
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Functional_equation
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Closed-form_expression
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Partition_function_(number_theory)
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Recurrence_relations
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Infinite_sequence
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Recurrence_relation
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Q-difference_polynomial
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Rational_functions
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Dilogarithm
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Contingency_tables
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Mathematics_and_plausible_reasoning
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Rational_function