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=4, b>=a > For fixed z and a=4, b=4





http://functions.wolfram.com/07.23.03.4207.01









  


  








Input Form





Hypergeometric2F1[4, 4, -(11/2), -z] == (1/(177408 (1 + z)^(27/2))) (Sqrt[1 + z] (177408 + z (2822400 + z (21980672 + z (114546176 + z (474253056 + z (1909347072 + z (13498844160 + z (-33441102447 + 4 (3110559271 - 177499799 z) z)))))))) + 14549535 z^(13/2) (-1615 + 2 z (969 + 4 z (-57 + 2 z))) ArcSinh[Sqrt[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["4", ",", "4", ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["177408", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["27", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["177408", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2822400", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21980672", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["114546176", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["474253056", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1909347072", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["13498844160", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33441102447"]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List["3110559271", "-", RowBox[List["177499799", " ", "z"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["14549535", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1615"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["969", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "57"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSinh", "[", SqrtBox["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> 4 </mn> <mo> , </mo> <mn> 4 </mn> </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[&quot;4&quot;, Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;4&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[RowBox[List[&quot;-&quot;, &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> 177408 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 14549535 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 57 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 969 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1615 </mn> </mrow> <mo> ) </mo> </mrow> <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> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <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> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3110559271 </mn> <mo> - </mo> <mrow> <mn> 177499799 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 33441102447 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 13498844160 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1909347072 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 474253056 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 114546176 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 21980672 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2822400 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 177408 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 4 </cn> <cn type='integer'> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <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'> 177408 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 27 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 14549535 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -57 </cn> </apply> </apply> <cn type='integer'> 969 </cn> </apply> </apply> <cn type='integer'> -1615 </cn> </apply> <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> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <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 /> <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'> 4 </cn> <apply> <plus /> <cn type='integer'> 3110559271 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 177499799 </cn> <ci> z </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <cn type='integer'> -33441102447 </cn> </apply> </apply> <cn type='integer'> 13498844160 </cn> </apply> </apply> <cn type='integer'> 1909347072 </cn> </apply> </apply> <cn type='integer'> 474253056 </cn> </apply> </apply> <cn type='integer'> 114546176 </cn> </apply> </apply> <cn type='integer'> 21980672 </cn> </apply> </apply> <cn type='integer'> 2822400 </cn> </apply> </apply> <cn type='integer'> 177408 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["4", ",", "4", ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["177408", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2822400", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21980672", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["114546176", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["474253056", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1909347072", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["13498844160", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33441102447"]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List["3110559271", "-", RowBox[List["177499799", " ", "z"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["14549535", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1615"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["969", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "57"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["177408", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["27", "/", "2"]]]]]]]]]]


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





2007-05-02