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=11/2, a2>=11/2 > For fixed z and a1=11/2, a2=11/2, b1>=-11/2 > For fixed z and a1=11/2, a2=11/2, b1=-11/2





http://functions.wolfram.com/07.25.03.ann9.01









  


  










Input Form





HypergeometricPFQ[{11/2, 11/2}, {-(11/2), -(5/2)}, z] == -((1/139244923125) (E^z (-139244923125 - 167093907750 z - 722010712500 z^2 - 9443310723000 z^3 + 158269463352000 z^4 - 1344169799280000 z^5 + 18770672223072000 z^6 + 170847530441280000 z^7 + 366778906933824000 z^8 + 350002403194752000 z^9 + 181581643589068800 z^10 + 56626673773178880 z^11 + 11240526521548800 z^12 + 1467489692712960 z^13 + 127938319810560 z^14 + 7444788019200 z^15 + 283782610944 z^16 + 6763970560 z^17 + 90963968 z^18 + 524288 z^19)))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["11", "2"], ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", "139244923125"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "139244923125"]], "-", RowBox[List["167093907750", " ", "z"]], "-", RowBox[List["722010712500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["9443310723000", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["158269463352000", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1344169799280000", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["18770672223072000", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["170847530441280000", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["366778906933824000", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["350002403194752000", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["181581643589068800", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["56626673773178880", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["11240526521548800", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["1467489692712960", " ", SuperscriptBox["z", "13"]]], "+", RowBox[List["127938319810560", " ", SuperscriptBox["z", "14"]]], "+", RowBox[List["7444788019200", " ", SuperscriptBox["z", "15"]]], "+", RowBox[List["283782610944", " ", SuperscriptBox["z", "16"]]], "+", RowBox[List["6763970560", " ", SuperscriptBox["z", "17"]]], "+", RowBox[List["90963968", " ", SuperscriptBox["z", "18"]]], "+", RowBox[List["524288", " ", SuperscriptBox["z", "19"]]]]], ")"]]]], ")"]]]]]]]]]]










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> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> <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> <mrow> <mo> - </mo> <mfrac> <mn> 5 </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;2&quot;], SubscriptBox[&quot;F&quot;, &quot;2&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;11&quot;, &quot;2&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[RowBox[List[&quot;-&quot;, 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[&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> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 139244923125 </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> 524288 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 19 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 90963968 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 18 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6763970560 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 17 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 283782610944 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 16 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7444788019200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 127938319810560 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1467489692712960 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11240526521548800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 56626673773178880 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 181581643589068800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 350002403194752000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 366778906933824000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 170847530441280000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 18770672223072000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1344169799280000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 158269463352000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9443310723000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 722010712500 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 167093907750 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 139244923125 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 11 <sep /> 2 </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> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 139244923125 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 524288 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 19 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 90963968 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 18 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6763970560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 17 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 283782610944 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 16 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7444788019200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 15 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 127938319810560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 14 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1467489692712960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11240526521548800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 56626673773178880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 181581643589068800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 350002403194752000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 366778906933824000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 170847530441280000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 18770672223072000 </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'> 1344169799280000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 158269463352000 </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'> 9443310723000 </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'> 722010712500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 167093907750 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -139244923125 </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[FractionBox["11", "2"], ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "139244923125"]], "-", RowBox[List["167093907750", " ", "z"]], "-", RowBox[List["722010712500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["9443310723000", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["158269463352000", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1344169799280000", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["18770672223072000", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["170847530441280000", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["366778906933824000", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["350002403194752000", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["181581643589068800", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["56626673773178880", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["11240526521548800", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["1467489692712960", " ", SuperscriptBox["z", "13"]]], "+", RowBox[List["127938319810560", " ", SuperscriptBox["z", "14"]]], "+", RowBox[List["7444788019200", " ", SuperscriptBox["z", "15"]]], "+", RowBox[List["283782610944", " ", SuperscriptBox["z", "16"]]], "+", RowBox[List["6763970560", " ", SuperscriptBox["z", "17"]]], "+", RowBox[List["90963968", " ", SuperscriptBox["z", "18"]]], "+", RowBox[List["524288", " ", SuperscriptBox["z", "19"]]]]], ")"]]]], "139244923125"]]]]]]]










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





2007-05-02