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





http://functions.wolfram.com/07.27.03.a889.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), -(5/2), 2}, {3, 4}, z] == 64/(1323 z^2) + (256 (-630 - 49223 z + 88888 z^2 + 768798 z^3 + 492934 z^4 + 42721 z^5) EllipticE[z])/(50426145 Pi z^3) + (1/(50426145 Pi z^3)) (128 (1260 + 59701 z - 217549 z^2 - 664014 z^3 + 416338 z^4 + 380009 z^5 + 24255 z^6) EllipticK[z])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List["3", ",", "4"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["64", RowBox[List["1323", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "630"]], "-", RowBox[List["49223", " ", "z"]], "+", RowBox[List["88888", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["768798", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["492934", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["42721", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], RowBox[List["50426145", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["50426145", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["128", " ", RowBox[List["(", RowBox[List["1260", "+", RowBox[List["59701", " ", "z"]], "-", RowBox[List["217549", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["664014", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["416338", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["380009", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["24255", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "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> 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> <mrow> <mo> - </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 4 </mn> </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[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]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[&quot;3&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[&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> <mn> 256 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 42721 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 492934 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 768798 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 88888 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 49223 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 630 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 50426145 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 128 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 24255 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 380009 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 416338 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 664014 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 217549 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 59701 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1260 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 50426145 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 64 </mn> <mrow> <mn> 1323 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </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> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> 2 </cn> </list> <list> <cn type='integer'> 3 </cn> <cn type='integer'> 4 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 42721 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 492934 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 768798 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 88888 </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'> 49223 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -630 </cn> </apply> <apply> <ci> EllipticE </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 50426145 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 24255 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 380009 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 416338 </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'> 664014 </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'> 217549 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 59701 </cn> <ci> z </ci> </apply> <cn type='integer'> 1260 </cn> </apply> <apply> <ci> EllipticK </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 50426145 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1323 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </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"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List["3", ",", "4"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["64", RowBox[List["1323", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "630"]], "-", RowBox[List["49223", " ", "z"]], "+", RowBox[List["88888", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["768798", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["492934", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["42721", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], RowBox[List["50426145", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox[RowBox[List["128", " ", RowBox[List["(", RowBox[List["1260", "+", RowBox[List["59701", " ", "z"]], "-", RowBox[List["217549", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["664014", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["416338", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["380009", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["24255", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]], RowBox[List["50426145", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]]]]]]]]










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





2007-05-02