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 8 and fixed z and a<0 > For fixed z and a=-37/8, b>=a > For fixed z and a=-37/8, b=-17/8





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









  


  








Input Form





Hypergeometric2F1[-(37/8), -(17/8), 9/2, -z] == -((256 (Sqrt[z] (-48 - 875 z - 9594 z^2 - 827541 z^3 + 2399540 z^4 - 1309893 z^5 + 93510 z^6 + 3621 z^7 + 144 z^8) Cos[(3 ArcTan[Sqrt[z]])/4] - 4 (-16 - 294 z - 3240 z^2 - 47853 z^3 + 444015 z^4 - 542256 z^5 + 124046 z^6 + 675 z^7 + 27 z^8) Sin[(3 ArcTan[Sqrt[z]])/4]))/(175450275 z^(7/2) (1 + z)^(3/8)))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["37", "8"]]], ",", RowBox[List["-", FractionBox["17", "8"]]], ",", FractionBox["9", "2"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "48"]], "-", RowBox[List["875", " ", "z"]], "-", RowBox[List["9594", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["827541", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2399540", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1309893", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["93510", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["3621", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["144", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], "4"], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16"]], "-", RowBox[List["294", " ", "z"]], "-", RowBox[List["3240", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["47853", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["444015", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["542256", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["124046", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["675", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["27", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], "4"], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["175450275", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "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> 37 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 17 </mn> <mn> 8 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> <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;37&quot;, &quot;8&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;17&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;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> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 175450275 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 256 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 144 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3621 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 93510 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1309893 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2399540 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 827541 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9594 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 875 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 48 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 27 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 675 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 124046 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 542256 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 444015 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 47853 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3240 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 294 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 16 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </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'> 37 <sep /> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 17 <sep /> 8 </cn> </apply> </list> <list> <cn type='rational'> 9 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 175450275 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 3 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3621 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 93510 </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'> 1309893 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2399540 </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'> 827541 </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'> 9594 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 875 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -48 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='rational'> 3 <sep /> 4 </cn> <apply> <arctan /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 675 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 124046 </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'> 542256 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 444015 </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'> 47853 </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'> 3240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 294 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -16 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='rational'> 3 <sep /> 4 </cn> <apply> <arctan /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </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["37", "8"]]], ",", RowBox[List["-", FractionBox["17", "8"]]], ",", FractionBox["9", "2"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "48"]], "-", RowBox[List["875", " ", "z"]], "-", RowBox[List["9594", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["827541", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2399540", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1309893", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["93510", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["3621", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["144", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], "4"], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16"]], "-", RowBox[List["294", " ", "z"]], "-", RowBox[List["3240", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["47853", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["444015", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["542256", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["124046", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["675", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["27", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], "4"], "]"]]]]]], ")"]]]], RowBox[List["175450275", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]]]]]]]]]


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





2007-05-02