Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Pochhammer_symbol> ?p ?o. }
Showing items 1 to 37 of
37
with 100 items per page.
- Pochhammer_symbol abstract "In mathematics, the Pochhammer symbol introduced by Leo August Pochhammer is the notation (x)n, where n is a non-negative integer. Depending on the context the Pochhammer symbol may represent either the rising factorial or the falling factorial as defined below. Care needs to be taken to check which interpretation is being used in any particular article. Pochhammer himself actually used (x)n with yet another meaning, namely to denote the binomial coefficient .In this article the Pochhammer symbol (x)n is used to represent the falling factorial (sometimes called the "descending factorial", "falling sequential product", "lower factorial"): In this article the symbol x(n) is used for the rising factorial (sometimes called the "Pochhammer function", "Pochhammer polynomial", "ascending factorial", "rising sequential product" or "upper factorial"):These conventions are used in combinatorics (Olver 1999, p. 101). However in the theory of special functions (in particular the hypergeometric function) the Pochhammer symbol (x)n is used to represent the rising factorial.A useful list of formulas for manipulating the rising factorial in this last notation is given in (Slater 1966, Appendix I). Knuth uses the term factorial powers to comprise rising and falling factorials.When x is a non-negative integer, then (x)n gives the number of n-permutations of an x-element set, or equivalently the number of injective functions from a set of size n to a set of size x. However, for these meanings other notations like xPn and P(x,n) are commonly used. The Pochhammer symbol serves mostly for more algebraic uses, for instance when x is an indeterminate, in which case (x)n designates a particular polynomial of degree n in x.".
- Pochhammer_symbol wikiPageID "230193".
- Pochhammer_symbol wikiPageRevisionID "604324769".
- Pochhammer_symbol hasPhotoCollection Pochhammer_symbol.
- Pochhammer_symbol title "Pochhammer Symbol".
- Pochhammer_symbol urlname "PochhammerSymbol".
- Pochhammer_symbol subject Category:Factorial_and_binomial_topics.
- Pochhammer_symbol subject Category:Finite_differences.
- Pochhammer_symbol subject Category:Gamma_and_related_functions.
- Pochhammer_symbol type Abstraction100002137.
- Pochhammer_symbol type Attribute100024264.
- Pochhammer_symbol type Difference104748836.
- Pochhammer_symbol type FiniteDifferences.
- Pochhammer_symbol type Quality104723816.
- Pochhammer_symbol comment "In mathematics, the Pochhammer symbol introduced by Leo August Pochhammer is the notation (x)n, where n is a non-negative integer. Depending on the context the Pochhammer symbol may represent either the rising factorial or the falling factorial as defined below. Care needs to be taken to check which interpretation is being used in any particular article.".
- Pochhammer_symbol label "Fattoriale crescente".
- Pochhammer_symbol label "Pochhammer symbol".
- Pochhammer_symbol label "Pochhammer-Symbol".
- Pochhammer_symbol label "Pochhammer-symbool".
- Pochhammer_symbol label "Potęgi kroczące".
- Pochhammer_symbol label "Symbole de Pochhammer".
- Pochhammer_symbol label "Símbolo de Pochhammer".
- Pochhammer_symbol label "Символ Похгаммера".
- Pochhammer_symbol label "阶乘幂".
- Pochhammer_symbol sameAs Pochhammer-Symbol.
- Pochhammer_symbol sameAs Símbolo_de_Pochhammer.
- Pochhammer_symbol sameAs Symbole_de_Pochhammer.
- Pochhammer_symbol sameAs Fattoriale_crescente.
- Pochhammer_symbol sameAs 포흐하머_기호.
- Pochhammer_symbol sameAs Pochhammer-symbool.
- Pochhammer_symbol sameAs Potęgi_kroczące.
- Pochhammer_symbol sameAs m.01hhf5.
- Pochhammer_symbol sameAs Q132335.
- Pochhammer_symbol sameAs Q132335.
- Pochhammer_symbol sameAs Pochhammer_symbol.
- Pochhammer_symbol wasDerivedFrom Pochhammer_symbol?oldid=604324769.
- Pochhammer_symbol isPrimaryTopicOf Pochhammer_symbol.