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=-9/2





http://functions.wolfram.com/07.25.03.an83.01









  


  








Input Form





HypergeometricPFQ[{5, 5}, {-(9/2), 2}, z] == (1/1088640) (1088640 - 3024000 z + 5184000 z^2 - 8467200 z^3 + 18063360 z^4 - 97542144 z^5 - 159324075 z^6 - 80666040 z^7 - 18947196 z^8 - 2324160 z^9 - 152144 z^10 - 4992 z^11 - 64 z^12) + (1/2177280) (E^z Sqrt[Pi] (-305162325 z^(11/2) - 384974010 z^(13/2) - 178292124 z^(15/2) - 40078296 z^(17/2) - 4795632 z^(19/2) - 309216 z^(21/2) - 10048 z^(23/2) - 128 z^(25/2)) 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["9", "2"]]], ",", "2"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "1088640"], RowBox[List["(", RowBox[List["1088640", "-", RowBox[List["3024000", " ", "z"]], "+", RowBox[List["5184000", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8467200", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18063360", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["97542144", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["159324075", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["80666040", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["18947196", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["2324160", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["152144", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["4992", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "12"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2177280"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "305162325"]], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["384974010", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "-", RowBox[List["178292124", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "-", RowBox[List["40078296", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "-", RowBox[List["4795632", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "-", RowBox[List["309216", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "-", RowBox[List["10048", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "-", RowBox[List["128", " ", SuperscriptBox["z", RowBox[List["25", "/", "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> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 2 </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;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[&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> 1088640 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 64 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4992 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 152144 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2324160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 18947196 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 80666040 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 159324075 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 97542144 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 18063360 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8467200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5184000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3024000 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1088640 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2177280 </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> <mrow> <mo> - </mo> <mn> 128 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10048 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 23 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 309216 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 21 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4795632 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 19 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 40078296 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 178292124 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 384974010 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 305162325 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </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'> 9 <sep /> 2 </cn> </apply> <cn type='integer'> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 1088640 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -64 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4992 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 152144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2324160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18947196 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 80666040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 159324075 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 97542144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 18063360 </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'> 8467200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5184000 </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'> 3024000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1088640 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2177280 </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'> -128 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 25 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10048 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 23 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 309216 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 21 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4795632 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40078296 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 178292124 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 384974010 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 305162325 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </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["9", "2"]]], ",", "2"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["1088640", "-", RowBox[List["3024000", " ", "z"]], "+", RowBox[List["5184000", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8467200", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18063360", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["97542144", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["159324075", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["80666040", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["18947196", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["2324160", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["152144", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["4992", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "12"]]]]], "1088640"], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "305162325"]], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["384974010", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "-", RowBox[List["178292124", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "-", RowBox[List["40078296", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "-", RowBox[List["4795632", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "-", RowBox[List["309216", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "-", RowBox[List["10048", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "-", RowBox[List["128", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], "2177280"]]]]]]]


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





2007-05-02