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=5, a2>=5 > For fixed z and a1=5, a2=5, b1>=-11/2 > For fixed z and a1=5, a2=5, b1=-3/2





http://functions.wolfram.com/07.25.03.an8v.01









  


  








Input Form





HypergeometricPFQ[{5, 5}, {-(3/2), 1}, z] == (1/55296) (55296 - 921600 z + 16588800 z^2 + 99471519 z^3 + 136060602 z^4 + 75533076 z^5 + 20547288 z^6 + 2953424 z^7 + 226272 z^8 + 8640 z^9 + 128 z^10) + (1/110592) (E^z Sqrt[Pi] (81162081 z^(5/2) + 291520944 z^(7/2) + 332746128 z^(9/2) + 169151424 z^(11/2) + 43842144 z^(13/2) + 6124800 z^(15/2) + 461056 z^(17/2) + 17408 z^(19/2) + 256 z^(21/2)) Erf[Sqrt[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["5", ",", "5"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], ",", "1"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "55296"], RowBox[List["(", RowBox[List["55296", "-", RowBox[List["921600", " ", "z"]], "+", RowBox[List["16588800", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["99471519", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["136060602", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["75533076", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["20547288", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["2953424", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["226272", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["8640", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["128", " ", SuperscriptBox["z", "10"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "110592"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["81162081", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["291520944", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["332746128", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["169151424", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["43842144", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["6124800", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["461056", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["17408", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["256", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], ")"]]]]]]]]]]








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> 5 </mn> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 1 </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;5&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;5&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;1&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> <mrow> <mfrac> <mn> 1 </mn> <mn> 55296 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 128 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8640 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 226272 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2953424 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20547288 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 75533076 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 136060602 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 99471519 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16588800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 921600 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 55296 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 110592 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 256 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 21 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 17408 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 19 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 461056 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6124800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 43842144 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 169151424 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 332746128 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 291520944 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 81162081 </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> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 5 </cn> <cn type='integer'> 5 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 55296 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 226272 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2953424 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 20547288 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 75533076 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 136060602 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 99471519 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16588800 </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'> 921600 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 55296 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 110592 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 21 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17408 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 461056 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6124800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 43842144 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 169151424 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 332746128 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 291520944 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 81162081 </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> </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["5", ",", "5"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], ",", "1"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["55296", "-", RowBox[List["921600", " ", "z"]], "+", RowBox[List["16588800", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["99471519", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["136060602", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["75533076", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["20547288", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["2953424", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["226272", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["8640", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["128", " ", SuperscriptBox["z", "10"]]]]], "55296"], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["81162081", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["291520944", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["332746128", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["169151424", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["43842144", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["6124800", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["461056", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["17408", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["256", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], "110592"]]]]]]]


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





2007-05-02