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 4 and fixed z > For fixed z and a=-23/4, b>=a > For fixed z and a=-23/4, b=-9/4





http://functions.wolfram.com/07.23.03.9251.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(9/4), 3/2, -z] == (1/(7735 Sqrt[z] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[2] (-437 + 16901 z - 61030 z^2 + 35202 z^3 + 471 z^4 + 57 z^5 + 4 z^6 + (437 - 12815 z + 20618 z^2 + 24042 z^3 - 10743 z^4 - 1027 z^5 - 120 z^6 - 8 z^7)/Sqrt[1 + z]))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", RowBox[List["-", FractionBox["9", "4"]]], ",", FractionBox["3", "2"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["7735", " ", SqrtBox["z"], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]], RowBox[List["(", RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "437"]], "+", RowBox[List["16901", " ", "z"]], "-", RowBox[List["61030", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["35202", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["471", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["57", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["4", " ", SuperscriptBox["z", "6"]]], "+", FractionBox[RowBox[List["437", "-", RowBox[List["12815", " ", "z"]], "+", RowBox[List["20618", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["24042", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["10743", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1027", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["120", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["8", " ", SuperscriptBox["z", "7"]]]]], SqrtBox[RowBox[List["1", "+", "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> 23 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 4 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mfrac> <mn> 3 </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;23&quot;, &quot;4&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;9&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[TagBox[TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, &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> <mfrac> <mn> 1 </mn> <mrow> <mn> 7735 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 57 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 471 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 35202 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 61030 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16901 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 120 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1027 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10743 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 24042 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20618 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12815 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 437 </mn> </mrow> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> - </mo> <mn> 437 </mn> </mrow> <mo> ) </mo> </mrow> </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'> 23 <sep /> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 4 </cn> </apply> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> </list> <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'> 7735 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 57 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 471 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35202 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 61030 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 16901 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -8 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1027 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10743 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 24042 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 20618 </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'> 12815 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 437 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -437 </cn> </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["23", "4"]]], ",", RowBox[List["-", FractionBox["9", "4"]]], ",", FractionBox["3", "2"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "437"]], "+", RowBox[List["16901", " ", "z"]], "-", RowBox[List["61030", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["35202", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["471", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["57", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["4", " ", SuperscriptBox["z", "6"]]], "+", FractionBox[RowBox[List["437", "-", RowBox[List["12815", " ", "z"]], "+", RowBox[List["20618", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["24042", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["10743", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1027", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["120", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["8", " ", SuperscriptBox["z", "7"]]]]], SqrtBox[RowBox[List["1", "+", "z"]]]]]], ")"]]]], RowBox[List["7735", " ", SqrtBox["z"], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]]]]]










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





2007-05-02