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=-11/2, b>=a > For fixed z and a=-11/2, b=-3/2





http://functions.wolfram.com/07.23.03.0821.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(3/2), 11/2, -z] == (1/(1342177280 z^(9/2))) (Sqrt[z] Sqrt[1 + z] (-24255 + 2 z (-199815 + 8 z (-217371 + 2 z (-760221 + 2 z (16854451 + 2 z (-9136825 + 32 z (19755 + 2 z (1061 + z (107 + 6 z))))))))) + 3465 (7 + 24 z (5 + z (45 + 32 z (10 + 7 z (15 + 8 z (-9 + 5 z)))))) ArcSinh[Sqrt[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["3", "2"]]], ",", FractionBox["11", "2"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1342177280", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24255"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "199815"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "217371"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "760221"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["16854451", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9136825"]], "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["19755", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1061", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["107", "+", RowBox[List["6", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["24", " ", "z", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["45", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["10", "+", RowBox[List["7", " ", "z", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSinh", "[", 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> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </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[RowBox[List[&quot;-&quot;, FractionBox[&quot;11&quot;, &quot;2&quot;]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;3&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[TagBox[TagBox[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[RowBox[List[&quot;-&quot;, &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> 1342177280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <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> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> <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> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <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> 32 </mn> <mo> &#8290; </mo> <mi> z </mi> <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> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 107 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1061 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 19755 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 9136825 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 16854451 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 760221 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 217371 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 199815 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 24255 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3465 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 24 </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> 32 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <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> 5 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </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> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='rational'> 11 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1342177280 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> <cn type='integer'> 107 </cn> </apply> </apply> <cn type='integer'> 1061 </cn> </apply> </apply> <cn type='integer'> 19755 </cn> </apply> </apply> <cn type='integer'> -9136825 </cn> </apply> </apply> <cn type='integer'> 16854451 </cn> </apply> </apply> <cn type='integer'> -760221 </cn> </apply> </apply> <cn type='integer'> -217371 </cn> </apply> </apply> <cn type='integer'> -199815 </cn> </apply> </apply> <cn type='integer'> -24255 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3465 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 24 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> z </ci> </apply> <cn type='integer'> -9 </cn> </apply> </apply> <cn type='integer'> 15 </cn> </apply> </apply> <cn type='integer'> 10 </cn> </apply> </apply> <cn type='integer'> 45 </cn> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <times /> <apply> <power /> <ci> sinh </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </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[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["3", "2"]]], ",", FractionBox["11", "2"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SqrtBox["z"], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24255"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "199815"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "217371"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "760221"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["16854451", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9136825"]], "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["19755", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1061", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["107", "+", RowBox[List["6", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["24", " ", "z", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["45", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["10", "+", RowBox[List["7", " ", "z", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["1342177280", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]


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





2007-05-02