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Pochhammer




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Pochhammer[a,n] > Series representations > Generalized power series > Expansions of (a+Epsilon)n at Epsilon==0/;a!=-m





http://functions.wolfram.com/06.10.06.0014.01









  


  








Input Form





Pochhammer[a + \[Epsilon], n] \[Proportional] Pochhammer[a, n] (1 + O[\[Epsilon]]) /; !(Element[a, Integers] && a <= 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a", "+", "\[Epsilon]"]], ",", "n"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", "\[Epsilon]", "]"]]]], ")"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List[RowBox[List["a", "\[Element]", "Integers"]], "\[And]", RowBox[List["a", "\[LessEqual]", "0"]]]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> &#1013; </mi> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;a&quot;, &quot;+&quot;, &quot;\[Epsilon]&quot;]], &quot;)&quot;]], &quot;n&quot;], Pochhammer] </annotation> </semantics> <mo> &#8733; </mo> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;a&quot;, &quot;)&quot;]], &quot;n&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#1013; </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> &#172; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[List[], Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> a </mi> <mo> &#8804; </mo> <mn> 0 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Pochhammer </ci> <apply> <plus /> <ci> a </ci> <ci> &#1013; </ci> </apply> <ci> n </ci> </apply> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> a </ci> <ci> n </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <ci> &#1013; </ci> </apply> </apply> </apply> </apply> <apply> <not /> <apply> <and /> <apply> <in /> <ci> a </ci> <integers /> </apply> <apply> <leq /> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a_", "+", "\[Epsilon]_"]], ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", "\[Epsilon]", "]"]]]], ")"]]]], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["a", "\[Element]", "Integers"]], "&&", RowBox[List["a", "\[LessEqual]", "0"]]]], ")"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2007-05-02