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=5, b>=a > For fixed z and a=5, b=5





http://functions.wolfram.com/07.23.03.4403.01









  


  








Input Form





Hypergeometric2F1[5, 5, -(7/2), z] == (1/(114688 (-1 + z)^14)) ((-(-1 + z)) (114688 + z (-2310144 + z (25493504 + z (-237600768 + z (3666493440 + z (23133380313 + 2 z (12540798883 + 4 z (823583643 + 38255054 z)))))))) + 765765 Sqrt[1 - z] z^(9/2) (12155 + 32 z (1105 + z (765 + 4 z (34 + z)))) ArcSin[Sqrt[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["5", ",", "5", ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["114688", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "14"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]], " ", RowBox[List["(", RowBox[List["114688", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2310144"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["25493504", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "237600768"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3666493440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["23133380313", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["12540798883", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["823583643", "+", RowBox[List["38255054", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["765765", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["12155", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["1105", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["765", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["34", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", 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> 5 </mn> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 7 </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;5&quot;, Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;5&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;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[&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> 114688 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 14 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 765765 </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> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <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> <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> <mi> z </mi> <mo> + </mo> <mn> 34 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 765 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1105 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 12155 </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> <mn> 2 </mn> <mo> &#8290; </mo> <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> <mn> 38255054 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 823583643 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 12540798883 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 23133380313 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3666493440 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 237600768 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 25493504 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2310144 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 114688 </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'> 5 </cn> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 114688 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 14 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 765765 </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'> 9 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 34 </cn> </apply> </apply> <cn type='integer'> 765 </cn> </apply> </apply> <cn type='integer'> 1105 </cn> </apply> </apply> <cn type='integer'> 12155 </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 /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 38255054 </cn> <ci> z </ci> </apply> <cn type='integer'> 823583643 </cn> </apply> </apply> <cn type='integer'> 12540798883 </cn> </apply> </apply> <cn type='integer'> 23133380313 </cn> </apply> </apply> <cn type='integer'> 3666493440 </cn> </apply> </apply> <cn type='integer'> -237600768 </cn> </apply> </apply> <cn type='integer'> 25493504 </cn> </apply> </apply> <cn type='integer'> -2310144 </cn> </apply> </apply> <cn type='integer'> 114688 </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["5", ",", "5", ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]], " ", RowBox[List["(", RowBox[List["114688", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2310144"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["25493504", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "237600768"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3666493440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["23133380313", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["12540798883", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["823583643", "+", RowBox[List["38255054", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["765765", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["12155", "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List["1105", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["765", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["34", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["114688", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "14"]]]]]]]]


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





2007-05-02