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=-7/2





http://functions.wolfram.com/07.23.03.0767.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(7/2), 4, z] == -((1/(9954945 Pi z^3)) (32 ((-56 + z (1533 + z (-31528 + z (-1648921 + z (-5585778 + z (-4480373 + z (-829508 + 91 z (-93 + 2 z)))))))) EllipticE[z] - (-1 + z) (56 + z (-1505 + z (30786 + z (1041853 + z (2962532 + z (1974633 + 91 z (3110 + z))))))) EllipticK[z])))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "4", ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["9954945", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "56"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1533", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "31528"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1648921"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5585778"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4480373"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "829508"]], "+", RowBox[List["91", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "93"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["56", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1505"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30786", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1041853", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2962532", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1974633", "+", RowBox[List["91", " ", "z", " ", RowBox[List["(", RowBox[List["3110", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "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> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mn> 4 </mn> <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[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;7&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[&quot;4&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> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 9954945 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 32 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <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> 91 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 93 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 829508 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 4480373 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 5585778 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1648921 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 31528 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1533 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 56 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> E </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <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> <mn> 91 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 3110 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1974633 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2962532 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1041853 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 30786 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1505 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 56 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </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'> 7 <sep /> 2 </cn> </apply> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 9954945 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <plus /> <apply> <times /> <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'> 91 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -93 </cn> </apply> </apply> <cn type='integer'> -829508 </cn> </apply> </apply> <cn type='integer'> -4480373 </cn> </apply> </apply> <cn type='integer'> -5585778 </cn> </apply> </apply> <cn type='integer'> -1648921 </cn> </apply> </apply> <cn type='integer'> -31528 </cn> </apply> </apply> <cn type='integer'> 1533 </cn> </apply> </apply> <cn type='integer'> -56 </cn> </apply> <apply> <times /> <exponentiale /> <ci> z </ci> </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 /> <cn type='integer'> 91 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 3110 </cn> </apply> </apply> <cn type='integer'> 1974633 </cn> </apply> </apply> <cn type='integer'> 2962532 </cn> </apply> </apply> <cn type='integer'> 1041853 </cn> </apply> </apply> <cn type='integer'> 30786 </cn> </apply> </apply> <cn type='integer'> -1505 </cn> </apply> </apply> <cn type='integer'> 56 </cn> </apply> <apply> <times /> <ci> K </ci> <ci> z </ci> </apply> </apply> </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["7", "2"]]], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "56"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1533", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "31528"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1648921"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5585778"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4480373"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "829508"]], "+", RowBox[List["91", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "93"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["56", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1505"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30786", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1041853", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2962532", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1974633", "+", RowBox[List["91", " ", "z", " ", RowBox[List["(", RowBox[List["3110", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["9954945", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]]]]]]]]










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





2007-05-02