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=-9/2, a2>=-9/2 > For fixed z and a1=-9/2, a2=2, b1>=-11/2 > For fixed z and a1=-9/2, a2=2, b1=-3/2





http://functions.wolfram.com/07.25.03.4076.01









  


  








Input Form





HypergeometricPFQ[{-(9/2), 2}, {-(3/2), 6}, -z] == (140 (-10296 + 11286 z - 5814 z^2 + 1615 z^3))/(46189 z^5) + (1/(138567 z^5)) ((8 (540540 - 51975 z - 17010 z^2 + 14280 z^3 - 8400 z^4 + 5616 z^5 - 5600 z^6 + 15616 z^7 + 5296 z^8 + 352 z^9))/E^z) + (64 Sqrt[Pi] (2261 z^(5/2) + 684 z^(7/2) + 44 z^(9/2)) Erf[Sqrt[z]])/138567








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], ",", "6"]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["140", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10296"]], "+", RowBox[List["11286", " ", "z"]], "-", RowBox[List["5814", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1615", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], RowBox[List["46189", " ", SuperscriptBox["z", "5"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["138567", " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["8", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List["540540", "-", RowBox[List["51975", " ", "z"]], "-", RowBox[List["17010", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["14280", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["8400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["5616", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["5600", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["15616", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["5296", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["352", " ", SuperscriptBox["z", "9"]]]]], ")"]]]], ")"]]]], "+", FractionBox[RowBox[List["64", " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["2261", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["684", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["44", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], "138567"]]]]]]]








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> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </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[RowBox[List[&quot;-&quot;, FractionBox[&quot;9&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[RowBox[List[&quot;-&quot;, FractionBox[&quot;3&quot;, &quot;2&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[RowBox[List[&quot;-&quot;, &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> 140 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1615 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5814 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11286 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 10296 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 46189 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 138567 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 352 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5296 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15616 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5616 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 14280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 17010 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 51975 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 540540 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 64 </mn> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 44 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 684 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2261 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erf </mi> <mo> &#8289; </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mn> 138567 </mn> </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'> 9 <sep /> 2 </cn> </apply> <cn type='integer'> 2 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> 6 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 140 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1615 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5814 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11286 </cn> <ci> z </ci> </apply> <cn type='integer'> -10296 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 46189 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 138567 </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'> 8 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 352 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15616 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5616 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 14280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 17010 </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'> 51975 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 540540 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 44 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 684 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2261 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Erf </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 138567 </cn> <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["9", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], ",", "6"]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["140", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10296"]], "+", RowBox[List["11286", " ", "z"]], "-", RowBox[List["5814", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1615", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], RowBox[List["46189", " ", SuperscriptBox["z", "5"]]]], "+", FractionBox[RowBox[List["8", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List["540540", "-", RowBox[List["51975", " ", "z"]], "-", RowBox[List["17010", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["14280", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["8400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["5616", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["5600", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["15616", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["5296", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["352", " ", SuperscriptBox["z", "9"]]]]], ")"]]]], RowBox[List["138567", " ", SuperscriptBox["z", "5"]]]], "+", FractionBox[RowBox[List["64", " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["2261", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["684", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["44", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], "138567"]]]]]]]


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





2007-05-02