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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] > Specific values > Specialized values > Cases with m==2 > Case {m,n,p,q}={2,1,2,2}





http://functions.wolfram.com/07.34.03.0827.01









  


  








Input Form





MeijerG[{{a}, {a + 1/2}}, {{a, a}, {}}, z] == (2 z^(-(1/2) + a) ArcCsch[Sqrt[z]])/(Sqrt[Pi] Sqrt[1 + 1/z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "a", "}"]], ",", RowBox[List["{", RowBox[List["a", "+", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a", ",", "a"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "a"]]], " ", RowBox[List["ArcCsch", "[", SqrtBox["z"], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], SqrtBox[RowBox[List["1", "+", FractionBox["1", "z"]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mi> a </mi> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi> a </mi> <mo> , </mo> <mi> a </mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;2&quot;]], RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;1&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[&quot;a&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;a&quot;, &quot;+&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[&quot;a&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;a&quot;, MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> a </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </mrow> </msqrt> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> csch </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> MeijerG </ci> <list> <list> <ci> a </ci> </list> <list> <apply> <plus /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </list> </list> <list> <list> <ci> a </ci> <ci> a </ci> </list> <list /> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <arccsch /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "a_", "}"]], ",", RowBox[List["{", RowBox[List["a_", "+", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a_", ",", "a_"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "a"]]], " ", RowBox[List["ArcCsch", "[", SqrtBox["z"], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "z"]]]]]]]]]]]


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





2001-10-29