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=2, a2>=2 > For fixed z and a1=2, a2=2, b1>=-11/2 > For fixed z and a1=2, a2=2, b1=6





http://functions.wolfram.com/07.25.03.ahj4.01









  


  








Input Form





HypergeometricPFQ[{2, 2}, {6, 6}, z] == (400 E^z (38 - 17 z + z^2))/z^5 + (1/(3 z^5)) (400 (-114 - 72 EulerGamma - 135 z + 162 EulerGamma z + 135 z^2 - 54 EulerGamma z^2 - 14 z^3 + 3 EulerGamma z^3)) - (400 (-24 + 54 z - 18 z^2 + z^3) ExpIntegralEi[z])/z^5 - (200 (-24 + 54 z - 18 z^2 + z^3) Log[1/z])/z^5 + (200 (-24 + 54 z - 18 z^2 + z^3) Log[z])/z^5








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["2", ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List["6", ",", "6"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["400", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List["38", "-", RowBox[List["17", " ", "z"]], "+", SuperscriptBox["z", "2"]]], ")"]]]], SuperscriptBox["z", "5"]], "+", RowBox[List[FractionBox["1", RowBox[List["3", " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["400", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "114"]], "-", RowBox[List["72", " ", "EulerGamma"]], "-", RowBox[List["135", " ", "z"]], "+", RowBox[List["162", " ", "EulerGamma", " ", "z"]], "+", RowBox[List["135", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["54", " ", "EulerGamma", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["14", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3", " ", "EulerGamma", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], ")"]]]], "-", FractionBox[RowBox[List["400", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["54", " ", "z"]], "-", RowBox[List["18", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", "z", "]"]]]], SuperscriptBox["z", "5"]], "-", FractionBox[RowBox[List["200", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["54", " ", "z"]], "-", RowBox[List["18", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", FractionBox["1", "z"], "]"]]]], SuperscriptBox["z", "5"]], "+", FractionBox[RowBox[List["200", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["54", " ", "z"]], "-", RowBox[List["18", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", "z", "]"]]]], SuperscriptBox["z", "5"]]]]]]]]








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> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mn> 6 </mn> <mo> , </mo> <mn> 6 </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;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;6&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;6&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> 400 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 38 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 400 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 54 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 135 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 162 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 135 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 72 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> - </mo> <mn> 114 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 400 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> - </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 54 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 200 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> - </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 54 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> ) </mo> </mrow> </mrow> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 200 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> - </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 54 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 2 </cn> <cn type='integer'> 2 </cn> </list> <list> <cn type='integer'> 6 </cn> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 17 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 38 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <eulergamma /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14 </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'> 54 </cn> <eulergamma /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 135 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 162 </cn> <eulergamma /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 135 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 72 </cn> <eulergamma /> </apply> </apply> <cn type='integer'> -114 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 54 </cn> <ci> z </ci> </apply> <cn type='integer'> -24 </cn> </apply> <apply> <ci> ExpIntegralEi </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 200 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 54 </cn> <ci> z </ci> </apply> <cn type='integer'> -24 </cn> </apply> <apply> <ln /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 200 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 54 </cn> <ci> z </ci> </apply> <cn type='integer'> -24 </cn> </apply> <apply> <ln /> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </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["2", ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List["6", ",", "6"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["400", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List["38", "-", RowBox[List["17", " ", "z"]], "+", SuperscriptBox["z", "2"]]], ")"]]]], SuperscriptBox["z", "5"]], "+", FractionBox[RowBox[List["400", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "114"]], "-", RowBox[List["72", " ", "EulerGamma"]], "-", RowBox[List["135", " ", "z"]], "+", RowBox[List["162", " ", "EulerGamma", " ", "z"]], "+", RowBox[List["135", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["54", " ", "EulerGamma", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["14", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3", " ", "EulerGamma", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], RowBox[List["3", " ", SuperscriptBox["z", "5"]]]], "-", FractionBox[RowBox[List["400", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["54", " ", "z"]], "-", RowBox[List["18", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", "z", "]"]]]], SuperscriptBox["z", "5"]], "-", FractionBox[RowBox[List["200", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["54", " ", "z"]], "-", RowBox[List["18", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", FractionBox["1", "z"], "]"]]]], SuperscriptBox["z", "5"]], "+", FractionBox[RowBox[List["200", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["54", " ", "z"]], "-", RowBox[List["18", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", "z", "]"]]]], SuperscriptBox["z", "5"]]]]]]]]


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





2007-05-02