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=2, a3>=2 > For fixed z and a1=-5/2, a2=2, a3=3 > For fixed z and a1=-5/2, a2=2, a3=3, b1=-7/2





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









  


  










Input Form





HypergeometricPFQ[{-(5/2), 2, 3}, {-(7/2), -(7/2)}, z] == (1/(3920 (-1 + z)^9)) (-3920 + 40080 z - 191232 z^2 + 574528 z^3 - 1084512 z^4 + 7416018 z^5 + 4659283 z^6 + 76230 z^7) + (1287 (22 z^(9/2) + 181 z^(11/2) + 52 z^(13/2)) ArcSin[Sqrt[z]])/ (112 Sqrt[1 - z] (-1 + z)^9)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", "2", ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["3920", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"]]]], RowBox[List["(", RowBox[List[RowBox[List["-", "3920"]], "+", RowBox[List["40080", " ", "z"]], "-", RowBox[List["191232", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["574528", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1084512", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["7416018", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["4659283", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["76230", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "+", FractionBox[RowBox[List["1287", " ", RowBox[List["(", RowBox[List[RowBox[List["22", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["181", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["52", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["112", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"]]]]]]]]]]










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> <mrow> <mo> - </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> </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[RowBox[List[&quot;-&quot;, FractionBox[&quot;5&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;2&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&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[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;7&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;7&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> <mfrac> <mrow> <mrow> <mn> 76230 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4659283 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7416018 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1084512 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 574528 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 191232 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 3920 </mn> </mrow> <mrow> <mn> 3920 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 9 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1287 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 52 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 181 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 22 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </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> </mrow> <mrow> <mn> 112 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 9 </mn> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 76230 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4659283 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7416018 </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'> 1084512 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 574528 </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'> 191232 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 40080 </cn> <ci> z </ci> </apply> <cn type='integer'> -3920 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 3920 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 9 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1287 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 52 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 181 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 22 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 112 </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> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 9 </cn> </apply> </apply> <cn type='integer'> -1 </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[RowBox[List["-", FractionBox["5", "2"]]], ",", "2", ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "3920"]], "+", RowBox[List["40080", " ", "z"]], "-", RowBox[List["191232", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["574528", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1084512", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["7416018", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["4659283", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["76230", " ", SuperscriptBox["z", "7"]]]]], RowBox[List["3920", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"]]]], "+", FractionBox[RowBox[List["1287", " ", RowBox[List["(", RowBox[List[RowBox[List["22", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["181", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["52", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["112", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"]]]]]]]]]]










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





2007-05-02