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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] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/07.34.16.0004.01









  


  








Input Form





Cos[(Subscript[b, 1] - Subscript[b, m + 1]) Pi] 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] - MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}}, {{Subscript[b, m + 1], Subscript[b, 2], \[Ellipsis], Subscript[b, m]}, {Subscript[b, 1], Subscript[b, m + 2], \[Ellipsis], Subscript[b, q]}}, z] == Sin[(Subscript[b, 1] - Subscript[b, m + 1]) Pi] MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p], Subscript[b, m + 1] - 1/2}}, {{Subscript[b, 1], Subscript[b, 2], \[Ellipsis], Subscript[b, m], Subscript[b, m + 1]}, {Subscript[b, m + 2], \[Ellipsis], Subscript[b, q], Subscript[b, m + 1] - 1/2}}, z]








Standard Form





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MathML Form







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</mo> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msubsup> <semantics> <mi> G </mi> <annotation encoding='Mathematica'> TagBox[&quot;G&quot;, MeijerG] </annotation> </semantics> <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> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> n </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <semantics> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mo> &#8230; </mo> <annotation encoding='Mathematica'> TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <msub> <mi> a </mi> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;a&quot;, &quot;n&quot;], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;a&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mo> &#8230; </mo> <annotation encoding='Mathematica'> TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mrow> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;p&quot;], &quot;,&quot;, RowBox[List[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;-&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <semantics> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mo> &#8230; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["b_", "1"], "-", SubscriptBox["b_", RowBox[List["m_", "+", "1"]]]]], ")"]], " ", "\[Pi]"]], "]"]], " ", 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_"]], "]"]]]], "-", 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_", RowBox[List["m_", "+", "1"]]], ",", SubscriptBox["b_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "m_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", RowBox[List["m_", "+", "2"]]], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]]]], "}"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["b", RowBox[List["m", "+", "1"]]]]], ")"]], " ", "\[Pi]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["aa", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "n"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "p"], ",", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "-", FractionBox["1", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["bb", "1"], ",", SubscriptBox["bb", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "m"], ",", SubscriptBox["b", RowBox[List["m", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "2"]]], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "q"], ",", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "-", FractionBox["1", "2"]]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]]]]]]


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





2007-05-02