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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] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.34.20.0018.02









  


  










Input Form





D[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]}}, w/z^(r/l)], {z, u}] == (l^\[Mu] r^u MeijerG[{{Subscript[a, 1]/l, \[Ellipsis], (Subscript[a, 1] + l - 1)/l, \[Ellipsis], Subscript[a, n]/l, \[Ellipsis], (Subscript[a, n] + l - 1)/l}, {(1 - u)/r, \[Ellipsis], (1 - u + r - 1)/r, Subscript[a, n + 1]/l, \[Ellipsis], (Subscript[a, n + 1] + l - 1)/l, \[Ellipsis], Subscript[a, p]/l, \[Ellipsis], (Subscript[a, p] + l - 1)/l}}, {{1/r, \[Ellipsis], r/r, Subscript[b, 1]/l, \[Ellipsis], (Subscript[b, 1] + l - 1)/l, \[Ellipsis], Subscript[b, m]/l, \[Ellipsis], (Subscript[b, m] + l - 1)/l}, {Subscript[b, m + 1]/l, \[Ellipsis], (Subscript[b, m + 1] + l - 1)/l, \[Ellipsis], Subscript[b, q]/l, \[Ellipsis], (Subscript[b, q] + l - 1)/l}}, (w^l l^(l (p - q)))/z^r])/((2 Pi)^((l - 1) SuperStar[c]) z^u) /; Element[u, Integers] && u >= 0 && SuperStar[c] == m + n - (p + q)/2 && \[Mu] == Sum[Subscript[b, j], {j, 1, q}] - Sum[Subscript[a, j], {j, 1, p}] + (p - q)/2 + 1










Standard Form





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MathML Form







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Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;r&quot;, &quot;r&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;l&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;l&quot;, &quot;+&quot;, SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;-&quot;, &quot;1&quot;]], &quot;l&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[SubscriptBox[&quot;b&quot;, &quot;m&quot;], &quot;l&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;l&quot;, &quot;+&quot;, SubscriptBox[&quot;b&quot;, &quot;m&quot;], &quot;-&quot;, &quot;1&quot;]], &quot;l&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;l&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;l&quot;, &quot;+&quot;, SubscriptBox[&quot;b&quot;, RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;-&quot;, &quot;1&quot;]], &quot;l&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[SubscriptBox[&quot;b&quot;, &quot;q&quot;], &quot;l&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;l&quot;, &quot;+&quot;, SubscriptBox[&quot;b&quot;, &quot;q&quot;], &quot;-&quot;, &quot;1&quot;]], &quot;l&quot;], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> u </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <msup> <mi> c </mi> <mo> * </mo> </msup> <mo> &#10869; </mo> <mrow> <mi> m </mi> <mo> + </mo> <mi> n </mi> <mo> - </mo> <mfrac> <mrow> <mi> p </mi> <mo> + </mo> <mi> q </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> &#956; </mi> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> q </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> + </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.