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 rational parameters with denominators 8 and fixed z and a<0 > For fixed z and a=-1/8, b>=a > For fixed z and a=-1/8, b=19/8





http://functions.wolfram.com/07.23.03.bwsb.01









  


  








Input Form





Hypergeometric2F1[-(1/8), 19/8, -(17/4), z] == (2 (3536 - 21632 z + 55191 z^2 - 74841 z^3 + 55383 z^4 - 8415 z^5 + 1530 z^6) + (7072 - 46800 z + 131130 z^2 - 199907 z^3 + 174237 z^4 - 58905 z^5 + 25925 z^6 - 4080 z^7)/Sqrt[1 - z])/ (7072 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z)^6)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["1", "8"]]], ",", FractionBox["19", "8"], ",", RowBox[List["-", FractionBox["17", "4"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["3536", "-", RowBox[List["21632", " ", "z"]], "+", RowBox[List["55191", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["74841", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["55383", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["8415", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1530", " ", SuperscriptBox["z", "6"]]]]], ")"]]]], "+", FractionBox[RowBox[List["7072", "-", RowBox[List["46800", " ", "z"]], "+", RowBox[List["131130", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["199907", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["174237", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["58905", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["25925", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["4080", " ", SuperscriptBox["z", "7"]]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["7072", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]]], ")"]]]]]]]]








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> 1 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 19 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 17 </mn> <mn> 4 </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[RowBox[List[&quot;-&quot;, FractionBox[&quot;1&quot;, &quot;8&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;19&quot;, &quot;8&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;17&quot;, &quot;4&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1530 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8415 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 55383 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 74841 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 55191 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 21632 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 3536 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4080 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 25925 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 58905 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 174237 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 199907 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 131130 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 46800 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 7072 </mn> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7072 </mn> <mo> &#8290; </mo> <mroot> <mn> 2 </mn> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='rational'> 19 <sep /> 8 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 17 <sep /> 4 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1530 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8415 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 55383 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 74841 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 55191 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 21632 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3536 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -4080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25925 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 58905 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 174237 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 199907 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 131130 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 46800 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 7072 </cn> </apply> <apply> <power /> <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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 7072 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["1", "8"]]], ",", FractionBox["19", "8"], ",", RowBox[List["-", FractionBox["17", "4"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["3536", "-", RowBox[List["21632", " ", "z"]], "+", RowBox[List["55191", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["74841", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["55383", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["8415", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1530", " ", SuperscriptBox["z", "6"]]]]], ")"]]]], "+", FractionBox[RowBox[List["7072", "-", RowBox[List["46800", " ", "z"]], "+", RowBox[List["131130", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["199907", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["174237", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["58905", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["25925", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["4080", " ", SuperscriptBox["z", "7"]]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], RowBox[List["7072", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]]]]]]]]


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





2007-05-02