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





http://functions.wolfram.com/07.27.03.acp9.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), 5/2, 5/2}, {-(3/2), 4}, z] == (32 (12600 + 1225 z + 1600 z^2 + 2304 z^3 + 4096 z^4 + 16384 z^5) EllipticE[z])/(10395 Pi z^3) - (32 (12600 - 5075 z + 200 z^2 + 384 z^3 + 1024 z^4 + 8192 z^5) EllipticK[z])/(10395 Pi z^3)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", FractionBox["5", "2"], ",", FractionBox["5", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], ",", "4"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["12600", "+", RowBox[List["1225", " ", "z"]], "+", RowBox[List["1600", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2304", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["16384", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], RowBox[List["10395", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["12600", "-", RowBox[List["5075", " ", "z"]], "+", RowBox[List["200", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]], RowBox[List["10395", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]]]]]]]]










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> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <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[FractionBox[&quot;5&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;5&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[TagBox[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;3&quot;, &quot;2&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> 32 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16384 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4096 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2304 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1225 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 12600 </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> 10395 </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> 32 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8192 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1024 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 384 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5075 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 12600 </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> 10395 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </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='rational'> 5 <sep /> 2 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> 4 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2304 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1225 </cn> <ci> z </ci> </apply> <cn type='integer'> 12600 </cn> </apply> <apply> <ci> EllipticE </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 10395 </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'> -1 </cn> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 200 </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'> 5075 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 12600 </cn> </apply> <apply> <ci> EllipticK </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 10395 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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"]]], ",", FractionBox["5", "2"], ",", FractionBox["5", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], ",", "4"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["12600", "+", RowBox[List["1225", " ", "z"]], "+", RowBox[List["1600", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2304", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["16384", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], RowBox[List["10395", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["12600", "-", RowBox[List["5075", " ", "z"]], "+", RowBox[List["200", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]], RowBox[List["10395", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]]]]]]]]










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





2007-05-02