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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,r] > Differentiation > Low-order differentiation > With respect to z





http://functions.wolfram.com/07.35.20.0001.01









  


  








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]}}, z, r], z] == (1/r) MeijerG[{{-r, Subscript[a, 1] - r, \[Ellipsis], Subscript[a, n] - r}, {Subscript[a, n + 1] - r, \[Ellipsis], Subscript[a, p] - r}}, {{Subscript[b, 1] - r, \[Ellipsis], Subscript[b, m] - r}, {1 - r, Subscript[b, m + 1] - r, \[Ellipsis], Subscript[b, q] - r}}, z, r]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "n"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "m"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]]]], "}"]], ",", "z", ",", "r"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", "r"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "r"]], ",", RowBox[List[SubscriptBox["a", "1"], "-", "r"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "n"], "-", "r"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "-", "r"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], "-", "r"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["b", "1"], "-", "r"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "m"], "-", "r"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "r"]], ",", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "-", "r"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], "-", "r"]]]], "}"]]]], "}"]], ",", "z", ",", "r"]], "]"]]]]]]]]








MathML Form







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</mo> <mi> z </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> r </mi> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mrow> <mi> p </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mrow> <mi> m </mi> <mo> , </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> , </mo> <mi> r </mi> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mo> - </mo> <mi> r </mi> </mrow> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mi> r </mi> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mi> n </mi> </msub> <mo> - </mo> <mi> r </mi> </mrow> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <mi> r </mi> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> - </mo> <mi> r </mi> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mi> r </mi> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> m </mi> </msub> <mo> - </mo> <mi> r </mi> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> r </mi> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <mi> r </mi> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> q </mi> </msub> <mo> - </mo> <mi> r </mi> </mrow> </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;p&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;,&quot;, RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]]]], RowBox[List[&quot;m&quot;, &quot;,&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;r&quot;, MeijerG, Rule[Editable, True]]]], MeijerG], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, &quot;r&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;1&quot;], &quot;-&quot;, &quot;r&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;, &quot;r&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;-&quot;, &quot;r&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;p&quot;], &quot;-&quot;, &quot;r&quot;]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;-&quot;, &quot;r&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;, &quot;r&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;r&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;-&quot;, &quot;r&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;q&quot;], &quot;-&quot;, &quot;r&quot;]], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "n_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a_", RowBox[List["n_", "+", "1"]]], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "m_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", RowBox[List["m_", "+", "1"]]], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]]]], "}"]], ",", "z_", ",", "r_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "r"]], ",", RowBox[List[SubscriptBox["aa", "1"], "-", "r"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["aa", "n"], "-", "r"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "-", "r"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["aa", "p"], "-", "r"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["bb", "1"], "-", "r"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["bb", "m"], "-", "r"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "r"]], ",", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "-", "r"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["bb", "q"], "-", "r"]]]], "}"]]]], "}"]], ",", "z", ",", "r"]], "]"]], "r"]]]]]


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





2001-10-29