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Pochhammer




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Pochhammer[a,n] > Identities > Recurrence identities > Distant neighbors





http://functions.wolfram.com/06.10.17.0003.02









  


  








Input Form





Pochhammer[a, n] == ((Gamma[a - m] Gamma[a + n])/(Gamma[a] Gamma[a - m + n])) Pochhammer[a - m, n]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "-", "m"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", "n"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["a", "-", "m", "+", "n"]], "]"]]]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a", "-", "m"]], ",", "n"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <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> &#10869; </mo> <mrow> <mfrac> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> m </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msub> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msub> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Pochhammer </ci> <ci> a </ci> <ci> n </ci> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Pochhammer", "[", RowBox[List["a_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "-", "m"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", "n"]], "]"]]]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a", "-", "m"]], ",", "n"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["a", "-", "m", "+", "n"]], "]"]]]]]]]]]


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





2001-10-29