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=3, b>=a > For fixed z and a=3, b=6





http://functions.wolfram.com/07.23.03.am7c.01









  


  








Input Form





Hypergeometric2F1[3, 6, 11/4, z] == (1/(10485760 z^(7/4))) (7 ((8 z^(3/4) (585 + 179780 z + 35520 z^2 - 8064 z^3 + 1024 z^4))/ (-1 + z)^6 - (1170 Sqrt[2] (-3 + 40 z + 320 z^2) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(25/4) - (1170 Sqrt[2] (-3 + 40 z + 320 z^2) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(25/4) + (585 Sqrt[2] (-3 + 40 z + 320 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(25/4) - (585 Sqrt[2] (-3 + 40 z + 320 z^2) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(25/4)))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", "6", ",", FractionBox["11", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["10485760", " ", SuperscriptBox["z", RowBox[List["7", "/", "4"]]]]]], RowBox[List["(", RowBox[List["7", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["585", "+", RowBox[List["179780", " ", "z"]], "+", RowBox[List["35520", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8064", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "-", FractionBox[RowBox[List["1170", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["40", " ", "z"]], "+", RowBox[List["320", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["25", "/", "4"]]]], "-", FractionBox[RowBox[List["1170", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["40", " ", "z"]], "+", RowBox[List["320", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["25", "/", "4"]]]], "+", FractionBox[RowBox[List["585", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["40", " ", "z"]], "+", RowBox[List["320", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["25", "/", "4"]]]], "-", FractionBox[RowBox[List["585", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["40", " ", "z"]], "+", RowBox[List["320", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["25", "/", "4"]]]]]], ")"]]]], ")"]]]]]]]]








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> 3 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mfrac> <mn> 11 </mn> <mn> 4 </mn> </mfrac> <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;3&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;6&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;11&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> <mfrac> <mn> 1 </mn> <mrow> <mn> 10485760 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1024 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8064 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 35520 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 179780 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 585 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1170 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 320 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mrow> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1170 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 320 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mfrac> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 585 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 320 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <msqrt> <mi> z </mi> </msqrt> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> - </mo> <mfrac> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 585 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 320 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <msqrt> <mi> z </mi> </msqrt> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> + </mo> <mfrac> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 3 </cn> <cn type='integer'> 6 </cn> </list> <list> <cn type='rational'> 11 <sep /> 4 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 10485760 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1024 </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'> 8064 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 35520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 179780 </cn> <ci> z </ci> </apply> <cn type='integer'> 585 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1170 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <ci> z </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <arctan /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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 /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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 /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </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'> 25 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1170 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <ci> z </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <arctan /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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 /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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 /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </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'> 25 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 585 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <ci> z </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </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 /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </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'> 25 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 585 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <ci> z </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </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> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </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 /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </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'> 25 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </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["3", ",", "6", ",", FractionBox["11", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["7", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["585", "+", RowBox[List["179780", " ", "z"]], "+", RowBox[List["35520", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8064", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "-", FractionBox[RowBox[List["1170", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["40", " ", "z"]], "+", RowBox[List["320", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["25", "/", "4"]]]], "-", FractionBox[RowBox[List["1170", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["40", " ", "z"]], "+", RowBox[List["320", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["25", "/", "4"]]]], "+", FractionBox[RowBox[List["585", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["40", " ", "z"]], "+", RowBox[List["320", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["25", "/", "4"]]]], "-", FractionBox[RowBox[List["585", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["40", " ", "z"]], "+", RowBox[List["320", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["25", "/", "4"]]]]]], ")"]]]], RowBox[List["10485760", " ", SuperscriptBox["z", RowBox[List["7", "/", "4"]]]]]]]]]]


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





2007-05-02