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},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=4, a2>=4 > For fixed z and a1=4, a2=11/2, b1>=-11/2 > For fixed z and a1=4, a2=11/2, b1=-11/2





http://functions.wolfram.com/07.25.03.amaa.01









  


  










Input Form





HypergeometricPFQ[{4, 11/2}, {-(11/2), 3}, z] == (1/29469825) (E^z (29469825 - 68762925 z + 89500950 z^2 - 90436500 z^3 + 86070600 z^4 - 96798240 z^5 + 237504960 z^6 + 427109760 z^7 + 186278400 z^8 + 34594560 z^9 + 3091968 z^10 + 130048 z^11 + 2048 z^12))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["4", ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "3"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "29469825"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List["29469825", "-", RowBox[List["68762925", " ", "z"]], "+", RowBox[List["89500950", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["90436500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["86070600", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["96798240", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["237504960", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["427109760", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["186278400", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["34594560", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["3091968", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["130048", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["2048", " ", SuperscriptBox["z", "12"]]]]], ")"]]]], ")"]]]]]]]]










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> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> , </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 3 </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;2&quot;], SubscriptBox[&quot;F&quot;, &quot;2&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[&quot;4&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;11&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;11&quot;, &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[&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> <mn> 1 </mn> <mn> 29469825 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2048 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 130048 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3091968 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 34594560 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 186278400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 427109760 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 237504960 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 96798240 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 86070600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 90436500 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 89500950 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 68762925 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 29469825 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 4 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='integer'> 3 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 29469825 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2048 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 130048 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3091968 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 34594560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 186278400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 427109760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 237504960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 96798240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 86070600 </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'> 90436500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 89500950 </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'> 68762925 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 29469825 </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["4", ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "3"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List["29469825", "-", RowBox[List["68762925", " ", "z"]], "+", RowBox[List["89500950", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["90436500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["86070600", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["96798240", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["237504960", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["427109760", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["186278400", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["34594560", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["3091968", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["130048", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["2048", " ", SuperscriptBox["z", "12"]]]]], ")"]]]], "29469825"]]]]]










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





2007-05-02