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=-7/2, b>=a > For fixed z and a=-7/2, b=-5/2





http://functions.wolfram.com/07.23.03.1579.01









  


  








Input Form





Hypergeometric2F1[-(7/2), -(5/2), 4, z] == (1/(1486485 Pi z^3)) (32 ((40 + z (-705 + z (8675 + z (215134 + z (300486 + z (65699 + 495 z)))))) EllipticE[z] + (-1 + z) (40 + z (-685 + z (8340 + z (126274 + z (138668 + 22275 z))))) EllipticK[z]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "4", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1486485", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["40", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "705"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8675", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["215134", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["300486", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["65699", "+", RowBox[List["495", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["40", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "685"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8340", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["126274", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["138668", "+", RowBox[List["22275", " ", "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> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 5 </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;7&quot;, &quot;2&quot;]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;5&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> <mfrac> <mn> 1 </mn> <mrow> <mn> 1486485 </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> <mn> 495 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 65699 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 300486 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 215134 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 8675 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 705 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 40 </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> <mn> 22275 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 138668 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 126274 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 8340 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 685 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 40 </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> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1486485 </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 /> <cn type='integer'> 495 </cn> <ci> z </ci> </apply> <cn type='integer'> 65699 </cn> </apply> </apply> <cn type='integer'> 300486 </cn> </apply> </apply> <cn type='integer'> 215134 </cn> </apply> </apply> <cn type='integer'> 8675 </cn> </apply> </apply> <cn type='integer'> -705 </cn> </apply> </apply> <cn type='integer'> 40 </cn> </apply> <apply> <times /> <exponentiale /> <ci> z </ci> </apply> </apply> <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 /> <cn type='integer'> 22275 </cn> <ci> z </ci> </apply> <cn type='integer'> 138668 </cn> </apply> </apply> <cn type='integer'> 126274 </cn> </apply> </apply> <cn type='integer'> 8340 </cn> </apply> </apply> <cn type='integer'> -685 </cn> </apply> </apply> <cn type='integer'> 40 </cn> </apply> <apply> <times /> <ci> K </ci> <ci> z </ci> </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["7", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["40", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "705"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8675", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["215134", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["300486", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["65699", "+", RowBox[List["495", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["40", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "685"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8340", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["126274", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["138668", "+", RowBox[List["22275", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["1486485", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]]]]]]


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





2007-05-02