Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Generating_function> ?p ?o. }
Showing items 1 to 50 of
50
with 100 items per page.
- Generating_function abstract "In mathematics, a generating function is a formal power series in one indeterminate, whose coefficients encode information about a sequence of numbers an that is indexed by the natural numbers. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem. One can generalize to formal power series in more than one indeterminate, to encode information about arrays of numbers indexed by several natural numbers.There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions and examples are given below. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require indices to start at 1 rather than 0), but the ease with which they can be handled may differ considerably. The particular generating function, if any, that is most useful in a given context will depend upon the nature of the sequence and the details of the problem being addressed.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations defined for formal power series. These expressions in terms of the indeterminate x may involve arithmetic operations, differentiation with respect to x and composition with (i.e., substitution into) other generating functions; since these operations are also defined for functions, the result looks like a function of x. Indeed, the closed form expression can often be interpreted as a function that can be evaluated at (sufficiently small) concrete values of x, and which has the formal power series as its Taylor series; this explains the designation "generating functions". However such interpretation is not required to be possible, because formal power series are not required to give a convergent series when a nonzero numeric value is substituted for x. Also, not all expressions that are meaningful as functions of x are meaningful as expressions designating formal power series; negative and fractional powers of x are examples of this.Generating functions are not functions in the formal sense of a mapping from a domain to a codomain; the name is merely traditional, and they are sometimes more correctly called generating series.".
- Generating_function wikiPageExternalLink book.pdf.
- Generating_function wikiPageExternalLink GeneratingFunctions.
- Generating_function wikiPageExternalLink 88b7b522437223ce.
- Generating_function wikiPageExternalLink read.php?12,360025.
- Generating_function wikiPageExternalLink 1200514223.
- Generating_function wikiPageExternalLink GeneratingFunctions.shtml.
- Generating_function wikiPageExternalLink FonctionsGeneratrices.pdf.
- Generating_function wikiPageExternalLink DownldGF.html.
- Generating_function wikiPageExternalLink DownldGF.html.
- Generating_function wikiPageID "160993".
- Generating_function wikiPageRevisionID "599020597".
- Generating_function hasPhotoCollection Generating_function.
- Generating_function id "p/g043900".
- Generating_function title "Generating function".
- Generating_function subject Category:Generating_functions.
- Generating_function type Abstraction100002137.
- Generating_function type Function113783816.
- Generating_function type GeneratingFunctions.
- Generating_function type MathematicalRelation113783581.
- Generating_function type Relation100031921.
- Generating_function comment "In mathematics, a generating function is a formal power series in one indeterminate, whose coefficients encode information about a sequence of numbers an that is indexed by the natural numbers. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem.".
- Generating_function label "Erzeugende Funktion".
- Generating_function label "Función generadora".
- Generating_function label "Funkcja tworząca".
- Generating_function label "Funzione generatrice".
- Generating_function label "Função geradora".
- Generating_function label "Generating function".
- Generating_function label "Série génératrice".
- Generating_function label "Voortbrengende functie".
- Generating_function label "Производящая функция последовательности".
- Generating_function label "دالة مولدة".
- Generating_function label "母函数".
- Generating_function label "母関数".
- Generating_function sameAs Vytvořující_funkce_(posloupnost).
- Generating_function sameAs Erzeugende_Funktion.
- Generating_function sameAs Función_generadora.
- Generating_function sameAs Série_génératrice.
- Generating_function sameAs Funzione_generatrice.
- Generating_function sameAs 母関数.
- Generating_function sameAs 생성함수_(수학).
- Generating_function sameAs Voortbrengende_functie.
- Generating_function sameAs Funkcja_tworząca.
- Generating_function sameAs Função_geradora.
- Generating_function sameAs m.0159kc.
- Generating_function sameAs Q860609.
- Generating_function sameAs Q860609.
- Generating_function sameAs Generating_function.
- Generating_function wasDerivedFrom Generating_function?oldid=599020597.
- Generating_function isPrimaryTopicOf Generating_function.