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 3 and fixed z > For fixed z and a=-17/3, b>=a > For fixed z and a=-17/3, b=14/3





http://functions.wolfram.com/07.23.03.4870.01









  


  








Input Form





Hypergeometric2F1[-(17/3), 14/3, -(11/2), -z] == (1/(216513 (1 + z)^(9/2))) ((216513 - 54675 z + 71658 z^2 - 125902 z^3 + 292325 z^4 - 1017159 z^5 + 9174880 z^6 + 57624112 z^7 + 98436416 z^8 + 69239040 z^9 + 17704960 z^10) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-72171 + 69012 z - 77994 z^2 + 104852 z^3 - 181467 z^4 + 480480 z^5 + 28837744 z^6 + 70456256 z^7 + 60386560 z^8 + 17704960 z^9) Sinh[ArcSinh[Sqrt[z]]/3])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["17", "3"]]], ",", FractionBox["14", "3"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["216513", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["216513", "-", RowBox[List["54675", " ", "z"]], "+", RowBox[List["71658", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["125902", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["292325", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1017159", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["9174880", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["57624112", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["98436416", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["69239040", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["17704960", " ", SuperscriptBox["z", "10"]]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]], "3"], "]"]]]], "+", RowBox[List[SqrtBox["z"], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "72171"]], "+", RowBox[List["69012", " ", "z"]], "-", RowBox[List["77994", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["104852", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["181467", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["480480", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["28837744", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["70456256", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["60386560", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["17704960", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]], "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> <mrow> <mo> - </mo> <mfrac> <mn> 17 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 14 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </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;17&quot;, &quot;3&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;14&quot;, &quot;3&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[RowBox[List[&quot;-&quot;, FractionBox[&quot;11&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[RowBox[List[&quot;-&quot;, &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> 216513 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 17704960 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 69239040 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 98436416 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 57624112 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9174880 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1017159 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 292325 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 125902 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 71658 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 54675 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 216513 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 17704960 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 60386560 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 70456256 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 28837744 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 480480 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 181467 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 104852 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 77994 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 69012 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 72171 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </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'> 17 <sep /> 3 </cn> </apply> <cn type='rational'> 14 <sep /> 3 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 216513 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 17704960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 69239040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 98436416 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 57624112 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9174880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1017159 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 292325 </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'> 125902 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 71658 </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'> 54675 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 216513 </cn> </apply> <apply> <times /> <ci> cosh </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <times /> <apply> <power /> <ci> sinh </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 17704960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 60386560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 70456256 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28837744 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 480480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 181467 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 104852 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 77994 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 69012 </cn> <ci> z </ci> </apply> <cn type='integer'> -72171 </cn> </apply> <apply> <times /> <ci> sinh </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <times /> <apply> <power /> <ci> sinh </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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["17", "3"]]], ",", FractionBox["14", "3"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["216513", "-", RowBox[List["54675", " ", "z"]], "+", RowBox[List["71658", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["125902", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["292325", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1017159", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["9174880", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["57624112", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["98436416", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["69239040", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["17704960", " ", SuperscriptBox["z", "10"]]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]], "3"], "]"]]]], "+", RowBox[List[SqrtBox["z"], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "72171"]], "+", RowBox[List["69012", " ", "z"]], "-", RowBox[List["77994", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["104852", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["181467", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["480480", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["28837744", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["70456256", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["60386560", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["17704960", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]], "3"], "]"]]]]]], RowBox[List["216513", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["9", "/", "2"]]]]]]]]]]


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





2007-05-02