Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a=6, b>=a > For fixed z and a=6, b=6





http://functions.wolfram.com/07.23.03.4508.01









  


  








Input Form





Hypergeometric2F1[6, 6, -(11/2), z] == (1/(10813440 (-1 + z)^18)) ((-(-1 + z)) (10813440 + z (-254607360 + z (3059220480 + z (-25878855680 + z (185228591104 + z (-1393947312128 + z (20217417170944 + z (138311350080655 + 4 z (48398906381455 + z (21124191140989 + 8 z (345961173494 + 9011219423 z))))))))))) + 334639305 Sqrt[1 - z] z^(13/2) (156009 + 2 z (260015 + 16 z (15295 + 4830 z + 460 z^2 + 8 z^3))) ArcSin[Sqrt[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["6", ",", "6", ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["10813440", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "18"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]], " ", RowBox[List["(", RowBox[List["10813440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "254607360"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3059220480", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "25878855680"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["185228591104", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1393947312128"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["20217417170944", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["138311350080655", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["48398906381455", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21124191140989", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["345961173494", "+", RowBox[List["9011219423", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["334639305", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List["156009", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["260015", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["15295", "+", RowBox[List["4830", " ", "z"]], "+", RowBox[List["460", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "3"]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["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> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;2&quot;], SubscriptBox[&quot;F&quot;, &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[&quot;6&quot;, Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;6&quot;, Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;11&quot;, &quot;2&quot;]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric2F1] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 10813440 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 18 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 334639305 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 460 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4830 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 15295 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 260015 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 156009 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9011219423 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 345961173494 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 21124191140989 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 48398906381455 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 138311350080655 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 20217417170944 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1393947312128 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 185228591104 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 25878855680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3059220480 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 254607360 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 10813440 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 6 </cn> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 10813440 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 18 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 334639305 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 460 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4830 </cn> <ci> z </ci> </apply> <cn type='integer'> 15295 </cn> </apply> </apply> <cn type='integer'> 260015 </cn> </apply> </apply> <cn type='integer'> 156009 </cn> </apply> <apply> <times /> <apply> <power /> <ci> sin </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 9011219423 </cn> <ci> z </ci> </apply> <cn type='integer'> 345961173494 </cn> </apply> </apply> <cn type='integer'> 21124191140989 </cn> </apply> </apply> <cn type='integer'> 48398906381455 </cn> </apply> </apply> <cn type='integer'> 138311350080655 </cn> </apply> </apply> <cn type='integer'> 20217417170944 </cn> </apply> </apply> <cn type='integer'> -1393947312128 </cn> </apply> </apply> <cn type='integer'> 185228591104 </cn> </apply> </apply> <cn type='integer'> -25878855680 </cn> </apply> </apply> <cn type='integer'> 3059220480 </cn> </apply> </apply> <cn type='integer'> -254607360 </cn> </apply> </apply> <cn type='integer'> 10813440 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["6", ",", "6", ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]], " ", RowBox[List["(", RowBox[List["10813440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "254607360"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3059220480", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "25878855680"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["185228591104", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1393947312128"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["20217417170944", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["138311350080655", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["48398906381455", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21124191140989", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["345961173494", "+", RowBox[List["9011219423", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["334639305", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List["156009", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["260015", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["15295", "+", RowBox[List["4830", " ", "z"]], "+", RowBox[List["460", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "3"]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["10813440", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "18"]]]]]]]]


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





2007-05-02