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
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
subject: Category:1730 introductions
subject: Category:Abraham de Moivre
subject: Category:Generating functions
math statement: Suppose that the generating function is represented by an infinite continued fraction of the form and that denotes the th convergent to this continued fraction expansion defined such that for all . Then: # the function is rational for all where we assume that one of divisibility criteria of is met, that is, for some ; and # if the integer divides the product , then we have .
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.
title: Generating function
hypernym: Series