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 integer and half-integer parameters and fixed z > For fixed z and a=2, b>=a > For fixed z and a=2, b=11/2





http://functions.wolfram.com/07.23.03.3726.01









  


  










Input Form





Hypergeometric2F1[2, 11/2, -(11/2), z] == (1/(21 (-1 + z)^13)) (-21 + z (315 + 13 z (-175 + z (825 + z (-2970 + z (9702 + z (-48510 + z (-103950 + z (-17325 + z (1155 + z (-99 + 5 z)))))))))))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", FractionBox["11", "2"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["21", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "13"]]]], RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "175"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["825", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2970"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["9702", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "48510"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "103950"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17325"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1155", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "99"]], "+", RowBox[List["5", " ", "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> <mn> 2 </mn> <mo> , </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <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;2&quot;, Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;11&quot;, &quot;2&quot;], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;11&quot;, &quot;2&quot;]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric2F1] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 21 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 13 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 13 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 99 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1155 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 17325 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 103950 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 48510 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 9702 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2970 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 825 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 175 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 315 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 21 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 2 </cn> <cn type='rational'> 11 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 13 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> z </ci> </apply> <cn type='integer'> -99 </cn> </apply> </apply> <cn type='integer'> 1155 </cn> </apply> </apply> <cn type='integer'> -17325 </cn> </apply> </apply> <cn type='integer'> -103950 </cn> </apply> </apply> <cn type='integer'> -48510 </cn> </apply> </apply> <cn type='integer'> 9702 </cn> </apply> </apply> <cn type='integer'> -2970 </cn> </apply> </apply> <cn type='integer'> 825 </cn> </apply> </apply> <cn type='integer'> -175 </cn> </apply> </apply> <cn type='integer'> 315 </cn> </apply> </apply> <cn type='integer'> -21 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", FractionBox["11", "2"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["-", "21"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "175"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["825", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2970"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["9702", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "48510"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "103950"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17325"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1155", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "99"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], RowBox[List["21", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "13"]]]]]]]]










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





2007-05-02