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variants of this functions
MeijerG






Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Identities > Functional identities > Relations with cut through poles





http://functions.wolfram.com/07.34.17.0019.01









  


  










Input Form





MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, z] == (-1)^(Sum[Subscript[bc, k], {k, 1, m}] + Sum[Subscript[ac, r], {r, 1, n}]) MeijerG[{{Subscript[a, 1] - Subscript[ac, 1], \[Ellipsis], Subscript[a, n] - Subscript[ac, n], Subscript[b, 1] + Subscript[bc, 1], \[Ellipsis], Subscript[b, m] + Subscript[bc, m]}, {Subscript[a, 1], \[Ellipsis], Subscript[a, p]}}, {{Subscript[a, 1] - Subscript[ac, 1], \[Ellipsis], Subscript[a, n] - Subscript[ac, n], Subscript[b, 1] + Subscript[bc, 1], \[Ellipsis], Subscript[b, m] + Subscript[bc, m]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}}, z] + Sum[(Product[If[j == k, 1, Gamma[Subscript[b, j] - Subscript[b, k]]], {j, 1, m}]/Product[Gamma[Subscript[a, j] - Subscript[b, k]], {j, n + 1, p}]) z^Subscript[b, k] Sum[((Product[Gamma[1 + Subscript[b, k] - Subscript[a, j] + i], {j, 1, n}] Product[Pochhammer[1 + Subscript[b, k] - Subscript[a, j], i], {j, n + 1, p}])/ (Product[Pochhammer[1 + Subscript[b, k] - Subscript[b, j], i], {j, 1, m}] Product[Gamma[1 + Subscript[b, k] - Subscript[b, j] + i], {j, m + 1, q}])) ((-1)^(p - m - n) z)^i, {i, 0, Floor[-Re[Subscript[b, k]] - \[Gamma]]}], {k, 1, m}] - Sum[(Product[If[j == k, 1, Gamma[Subscript[a, k] - Subscript[a, j]]], {j, 1, n}]/Product[Gamma[Subscript[a, k] - Subscript[b, j]], {j, m + 1, q}]) z^(Subscript[a, k] - 1) Sum[((Product[Gamma[1 - Subscript[a, k] + Subscript[b, j] + i], {j, 1, m}] Product[Pochhammer[1 + Subscript[b, j] - Subscript[a, k], i], {j, m + 1, q}])/ (Product[Pochhammer[1 + Subscript[a, j] - Subscript[a, k], i], {j, 1, n}] Product[Gamma[1 + Subscript[a, j] - Subscript[a, k] + i], {j, n + 1, p}])) ((-1)^(q - m - n)/z)^i, {i, 0, Floor[\[Gamma] + Re[Subscript[a, k]]] - 1}], {k, 1, n}] /; Subscript[ac, k] = UnitStep[Floor[\[Gamma] + Re[Subscript[a, k]]]] Floor[\[Gamma] + Re[Subscript[a, k]]] && Subscript[bc, k] = UnitStep[Floor[-Re[Subscript[b, k]] - \[Gamma]] + 1] (Floor[-Re[Subscript[b, k]] - \[Gamma]] + 1)










Standard Form





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MathML Form







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</mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mrow> <munderover> <mrow> <mtext> </mtext> <mo> &#8719; </mo> </mrow> <munder> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </munder> <mi> n </mi> </munderover> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> q </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mrow> <mo> &#8970; </mo> <mrow> <mi> &#947; </mi> <mo> + </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#8971; </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> m </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> i </mi> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> q </mi> </munderover> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;]]], &quot;+&quot;, SubscriptBox[&quot;b&quot;, &quot;j&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;j&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> p </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> i </mi> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mi> q </mi> </mrow> </msup> <mi> z </mi> </mfrac> <mo> ) </mo> </mrow> <mi> i </mi> </msup> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> m </mi> </munderover> <mrow> <mfrac> <mrow> <munderover> <mrow> <mtext> </mtext> <mo> &#8719; </mo> </mrow> <munder> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </munder> <mi> m </mi> </munderover> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> p </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> z </mi> <msub> <mi> b </mi> <mi> k </mi> </msub> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#947; </mi> </mrow> <mo> - </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> i </mi> <mo> - </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> + </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> p </mi> </munderover> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;j&quot;]]], &quot;+&quot;, SubscriptBox[&quot;b&quot;, &quot;k&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> m </mi> </munderover> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;j&quot;]]], &quot;+&quot;, SubscriptBox[&quot;b&quot;, &quot;k&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> q </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> i </mi> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> <mo> + </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mi> p </mi> </mrow> </msup> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msup> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <msub> <mi> ac </mi> <mi> k </mi> </msub> </mrow> <mo> = </mo> <mrow> <mrow> <mrow> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mo> &#8970; </mo> <mrow> <mi> &#947; </mi> <mo> + </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#8971; </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mrow> <mi> &#947; </mi> <mo> + </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#8971; </mo> </mrow> </mrow> <mo> &#8743; </mo> <msub> <mi> bc </mi> <mi> k </mi> </msub> </mrow> <mo> = </mo> <mrow> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mo> &#8970; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#947; </mi> </mrow> <mo> - </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#8971; </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; 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</mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> m </mi> </msub> <mo> + </mo> <msub> <mi> bc </mi> <mi> m </mi> </msub> </mrow> <mo> , </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;m&quot;, &quot;+&quot;, &quot;p&quot;]], &quot;,&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;m&quot;, &quot;+&quot;, &quot;q&quot;]]]], RowBox[List[RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;m&quot;]], &quot;,&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;m&quot;]]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;ac&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;n&quot;], &quot;-&quot;, SubscriptBox[&quot;ac&quot;, &quot;n&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;+&quot;, SubscriptBox[&quot;bc&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;m&quot;], &quot;+&quot;, SubscriptBox[&quot;bc&quot;, &quot;m&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;p&quot;], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;ac&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;n&quot;], &quot;-&quot;, SubscriptBox[&quot;ac&quot;, &quot;n&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;+&quot;, SubscriptBox[&quot;bc&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;m&quot;], &quot;+&quot;, SubscriptBox[&quot;bc&quot;, &quot;m&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;q&quot;], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mrow> <munderover> <mrow> <mtext> </mtext> <mo> &#8719; </mo> </mrow> <munder> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </munder> <mi> n </mi> </munderover> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> q </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; 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</mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;j&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> p </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> i </mi> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> &#8290; 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Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.