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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=-3/8, b>=a > For fixed z and a=-3/8, b=41/8





http://functions.wolfram.com/07.23.03.bw2x.01









  


  








Input Form





Hypergeometric2F1[-(3/8), 41/8, 9/8, z] == (2805 - 14960 z + 26400 z^2 - 19712 z^3 + 5376 z^4)/(2805 (1 - z)^(29/8))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["3", "8"]]], ",", FractionBox["41", "8"], ",", FractionBox["9", "8"], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["2805", "-", RowBox[List["14960", " ", "z"]], "+", RowBox[List["26400", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["19712", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5376", " ", SuperscriptBox["z", "4"]]]]], RowBox[List["2805", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["29", "/", "8"]]]]]]]]]]








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> 3 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 41 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mn> 9 </mn> <mn> 8 </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[RowBox[List[&quot;-&quot;, FractionBox[&quot;3&quot;, &quot;8&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;41&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[FractionBox[&quot;9&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[&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> <mfrac> <mrow> <mrow> <mn> 5376 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 19712 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 26400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14960 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2805 </mn> </mrow> <mrow> <mn> 2805 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 29 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <cn type='rational'> 41 <sep /> 8 </cn> </list> <list> <cn type='rational'> 9 <sep /> 8 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 5376 </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'> 19712 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 26400 </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'> 14960 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 2805 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2805 </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'> 29 <sep /> 8 </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["3", "8"]]], ",", FractionBox["41", "8"], ",", FractionBox["9", "8"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2805", "-", RowBox[List["14960", " ", "z"]], "+", RowBox[List["26400", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["19712", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5376", " ", SuperscriptBox["z", "4"]]]]], RowBox[List["2805", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["29", "/", "8"]]]]]]]]]]


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





2007-05-02