دالة مولدة
Genererande funktion
Funció generatriu
Examples of generating functions
생성함수 (수학)
Генератриса
Производящая функция последовательности
母函数
Funzione generatrice
Fungsi pembangkit
Erzeugende Funktion
Funkcja tworząca
Voortbrengende functie
Generating function
Vytvořující funkce (posloupnost)
Função geradora
Série génératrice
母関数
Función generadora
Mathematics and plausible reasoning
Generatingfunctionology
A generating function is a clothesline on which we hang up a sequence of numbers for display.
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.
Theorem: congruences for series generated by expansions of continued fractions
formal power series with coefficients that encode information about a sequence
série formelle dont les coefficients codent une suite
szereg formalny, w którym współczynniki przy poszczególnych potęgach odpowiadają elementom danego ciągu indeksowanego liczbami naturalnymi
Fonksiyon
Art von formaler Potenzreihe
formala potencoserio kies koeficientoj reprezentas iun nombrovicon
조합론의 개념
serie formal de potencias con coeficientes que codifican información sobre unha secuencia
形式冪級數，其系數隱含某數列的資訊
tipo di serie formale di potenze
یک سری توانی در ریاضیات
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 .