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
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=5/2, a2>=5/2 > For fixed z and a1=5/2, a2=4, a3>=4 > For fixed z and a1=5/2, a2=4, a3=4 > For fixed z and a1=5/2, a2=4, a3=4, b1=-5/2





http://functions.wolfram.com/07.27.03.auo7.01









  


  










Input Form





HypergeometricPFQ[{5/2, 4, 4}, {-(5/2), 3/2}, z] == (1/(2304 (-1 + z)^11)) (-2304 + 49920 z - 683776 z^2 + 13733120 z^3 + 108374750 z^4 + 139601821 z^5 + 42252796 z^6 + 2213908 z^7) + (5005 z^(7/2) (858 + 3003 z + 2418 z^2 + 488 z^3 + 16 z^4) ArcSin[Sqrt[z]])/ (256 Sqrt[1 - z] (-1 + 11 z - 55 z^2 + 165 z^3 - 330 z^4 + 462 z^5 - 462 z^6 + 330 z^7 - 165 z^8 + 55 z^9 - 11 z^10 + z^11))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", "4", ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["2304", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "11"]]]], RowBox[List["(", RowBox[List[RowBox[List["-", "2304"]], "+", RowBox[List["49920", " ", "z"]], "-", RowBox[List["683776", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13733120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["108374750", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["139601821", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["42252796", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["2213908", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["5005", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["858", "+", RowBox[List["3003", " ", "z"]], "+", RowBox[List["2418", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["488", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["16", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["256", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["11", " ", "z"]], "-", RowBox[List["55", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["165", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["330", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["462", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["462", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["330", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["165", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["55", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["11", " ", SuperscriptBox["z", "10"]]], "+", SuperscriptBox["z", "11"]]], ")"]]]], ")"]]]]]]]]]]










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> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 3 </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;3&quot;], SubscriptBox[&quot;F&quot;, &quot;2&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;5&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;4&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&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[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;5&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&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> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 5005 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 488 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2418 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3003 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 858 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 256 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 11 </mn> </msup> <mo> - </mo> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 55 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 165 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 330 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 462 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 462 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 330 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 165 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 55 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2304 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 11 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2213908 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 42252796 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 139601821 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 108374750 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13733120 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 683776 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 49920 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 2304 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 5 <sep /> 2 </cn> <cn type='integer'> 4 </cn> <cn type='integer'> 4 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 5005 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 488 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2418 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3003 </cn> <ci> z </ci> </apply> <cn type='integer'> 858 </cn> </apply> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 55 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 165 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 330 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 462 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 462 </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'> 330 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 165 </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'> 55 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2304 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 11 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2213908 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 42252796 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 139601821 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 108374750 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13733120 </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'> 683776 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 49920 </cn> <ci> z </ci> </apply> <cn type='integer'> -2304 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", "4", ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "2304"]], "+", RowBox[List["49920", " ", "z"]], "-", RowBox[List["683776", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13733120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["108374750", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["139601821", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["42252796", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["2213908", " ", SuperscriptBox["z", "7"]]]]], RowBox[List["2304", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "11"]]]], "+", FractionBox[RowBox[List["5005", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["858", "+", RowBox[List["3003", " ", "z"]], "+", RowBox[List["2418", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["488", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["16", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["256", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["11", " ", "z"]], "-", RowBox[List["55", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["165", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["330", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["462", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["462", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["330", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["165", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["55", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["11", " ", SuperscriptBox["z", "10"]]], "+", SuperscriptBox["z", "11"]]], ")"]]]]]]]]]]]










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





2007-05-02