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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > Values at fixed points > Values at z==-1





http://functions.wolfram.com/07.23.03.0617.01









  


  








Input Form





Hypergeometric2F1[5/6, 1, 17/6, -1] == (11/18) (5 Pi - 5 Sqrt[3] Log[2 + Sqrt[3]] - 3)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "6"], ",", "1", ",", FractionBox["17", "6"], ",", RowBox[List["-", "1"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["11", "18"], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", "\[Pi]"]], "-", RowBox[List["5", SqrtBox["3"], " ", RowBox[List["Log", "[", RowBox[List["2", "+", SqrtBox["3"]]], "]"]]]], "-", "3"]], ")"]]]]]]]]








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> <mfrac> <mn> 5 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mfrac> <mn> 17 </mn> <mn> 6 </mn> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;5&quot;, &quot;6&quot;], Hypergeometric2F1, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;1&quot;, Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[FractionBox[&quot;17&quot;, &quot;6&quot;], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;1&quot;]], Hypergeometric2F1, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 11 </mn> <mn> 18 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <cn type='rational'> 5 <sep /> 6 </cn> <cn type='integer'> 1 </cn> <cn type='rational'> 17 <sep /> 6 </cn> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <cn type='rational'> 11 <sep /> 18 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <pi /> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -3 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "6"], ",", "1", ",", FractionBox["17", "6"], ",", RowBox[List["-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["11", "18"], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", "\[Pi]"]], "-", RowBox[List["5", " ", SqrtBox["3"], " ", RowBox[List["Log", "[", RowBox[List["2", "+", SqrtBox["3"]]], "]"]]]], "-", "3"]], ")"]]]]]]]]


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





2001-10-29