Pochhammer[a, m n] == m^(m n) Product[Pochhammer[(a + j)/m, n], {j, 0, m - 1}] /; Element[m, Integers] && m > 0

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<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> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;a&quot;, &quot;)&quot;]], RowBox[List[&quot;m&quot;, &quot; &quot;, &quot;n&quot;]]], Pochhammer] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <msup> <mi> m </mi> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> j </mi> </mrow> <mi> m </mi> </mfrac> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, FractionBox[RowBox[List[&quot;a&quot;, &quot;+&quot;, &quot;j&quot;]], &quot;m&quot;], &quot;)&quot;]], &quot;n&quot;], Pochhammer] </annotation> </semantics> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Pochhammer </ci> <ci> a </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <times /> <apply> <power /> <ci> m </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <product /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <ci> Pochhammer </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> j </ci> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02