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=-21/4, b>=a > For fixed z and a=-21/4, b=13/4





http://functions.wolfram.com/07.23.03.a8qn.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 13/4, 5/2, z] == (1/(216315 z^(3/2))) (2 ((1 - Sqrt[z])^(9/2) (442 + 1989 Sqrt[z] + 15912 z + 112920 z^(3/2) + 229680 z^2 - 125136 z^(5/2) - 1015872 z^3 - 1400256 z^(7/2) - 823680 z^4 - 183040 z^(9/2)) - (1 + Sqrt[z])^(9/2) (442 - 1989 Sqrt[z] + 15912 z - 112920 z^(3/2) + 229680 z^2 + 125136 z^(5/2) - 1015872 z^3 + 1400256 z^(7/2) - 823680 z^4 + 183040 z^(9/2))))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["21", "4"]]], ",", FractionBox["13", "4"], ",", FractionBox["5", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["216315", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["442", "+", RowBox[List["1989", " ", SqrtBox["z"]]], "+", RowBox[List["15912", " ", "z"]], "+", RowBox[List["112920", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["229680", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["125136", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["1015872", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1400256", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["823680", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["183040", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["442", "-", RowBox[List["1989", " ", SqrtBox["z"]]], "+", RowBox[List["15912", " ", "z"]], "-", RowBox[List["112920", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["229680", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["125136", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["1015872", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1400256", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["823680", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["183040", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]








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> 21 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 13 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mn> 5 </mn> <mn> 2 </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;21&quot;, &quot;4&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;13&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;5&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[&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> 216315 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 183040 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 823680 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1400256 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1015872 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 125136 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 229680 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 112920 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15912 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 1989 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mn> 442 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 183040 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 823680 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1400256 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1015872 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 125136 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 229680 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 112920 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15912 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 1989 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mn> 442 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </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'> 21 <sep /> 4 </cn> </apply> <cn type='rational'> 13 <sep /> 4 </cn> </list> <list> <cn type='rational'> 5 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 216315 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -183040 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 823680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1400256 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1015872 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 125136 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 229680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 112920 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15912 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 1989 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 442 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 183040 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 823680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1400256 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1015872 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 125136 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 229680 </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'> 112920 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15912 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1989 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 442 </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[RowBox[List["-", FractionBox["21", "4"]]], ",", FractionBox["13", "4"], ",", FractionBox["5", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["442", "+", RowBox[List["1989", " ", SqrtBox["z"]]], "+", RowBox[List["15912", " ", "z"]], "+", RowBox[List["112920", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["229680", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["125136", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["1015872", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1400256", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["823680", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["183040", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["442", "-", RowBox[List["1989", " ", SqrtBox["z"]]], "+", RowBox[List["15912", " ", "z"]], "-", RowBox[List["112920", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["229680", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["125136", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["1015872", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1400256", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["823680", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["183040", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]]]]]], ")"]]]], RowBox[List["216315", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]]]]


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





2007-05-02