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Pochhammer




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Pochhammer[a,n] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/06.10.16.0008.01









  


  








Input Form





Pochhammer[a, n] Pochhammer[a + 1/2, n] == Pochhammer[2 a, 2 n]/4^n








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a", "+", FractionBox["1", "2"]]], ",", "n"]], "]"]]]], "\[Equal]", FractionBox[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["2", "a"]], ",", RowBox[List["2", "n"]]]], "]"]], SuperscriptBox["4", "n"]]]]]]








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> <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> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;a&quot;, &quot;+&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], &quot;)&quot;]], &quot;n&quot;], Pochhammer] </annotation> </semantics> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mn> 4 </mn> <mi> n </mi> </msup> </mfrac> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;a&quot;]], &quot;)&quot;]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;n&quot;]]], Pochhammer] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> a </ci> <ci> n </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> n </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <cn type='integer'> 4 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a_", ",", "n_"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a_", "+", FractionBox["1", "2"]]], ",", "n_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["2", " ", "a"]], ",", RowBox[List["2", " ", "n"]]]], "]"]], SuperscriptBox["4", "n"]]]]]]


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





2001-10-29