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





http://functions.wolfram.com/07.25.03.akm6.01









  


  










Input Form





HypergeometricPFQ[{3, 11/2}, {-(11/2), -(3/2)}, -z] == (1/29469825) (29469825 - 58939650 z + 340540200 z^2 + 2432430000 z^3 + 8270262000 z^4 + 29331862560 z^5 + 234654900480 z^6 - 673428349440 z^7 + 569506049280 z^8 - 225104140800 z^9 + 48455497728 z^10 - 6064521216 z^11 + 449691648 z^12 - 19310592 z^13 + 440320 z^14 - 4096 z^15) + (1/29469825) ((1024 Sqrt[Pi] (-424116000 z^(13/2) + 865196640 z^(15/2) - 648149040 z^(17/2) + 240997680 z^(19/2) - 50083110 z^(21/2) + 6133050 z^(23/2) - 448371 z^(25/2) + 19071 z^(27/2) - 432 z^(29/2) + 4 z^(31/2)) Erfi[Sqrt[z]])/E^z)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["3", ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "29469825"], RowBox[List["(", RowBox[List["29469825", "-", RowBox[List["58939650", " ", "z"]], "+", RowBox[List["340540200", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2432430000", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["8270262000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["29331862560", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["234654900480", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["673428349440", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["569506049280", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["225104140800", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["48455497728", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["6064521216", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["449691648", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["19310592", " ", SuperscriptBox["z", "13"]]], "+", RowBox[List["440320", " ", SuperscriptBox["z", "14"]]], "-", RowBox[List["4096", " ", SuperscriptBox["z", "15"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "29469825"], RowBox[List["(", RowBox[List["1024", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "424116000"]], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["865196640", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "-", RowBox[List["648149040", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["240997680", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "-", RowBox[List["50083110", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "+", RowBox[List["6133050", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "-", RowBox[List["448371", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]], "+", RowBox[List["19071", " ", SuperscriptBox["z", RowBox[List["27", "/", "2"]]]]], "-", RowBox[List["432", " ", SuperscriptBox["z", RowBox[List["29", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["31", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erfi", "[", 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> 3 </mn> <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> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> </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[&quot;3&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;3&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[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> <mrow> <mfrac> <mn> 1 </mn> <mn> 29469825 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4096 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 440320 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 19310592 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 449691648 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6064521216 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 48455497728 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 225104140800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 569506049280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 673428349440 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 234654900480 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 29331862560 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8270262000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2432430000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 340540200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 58939650 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 29469825 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 29469825 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1024 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 31 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 432 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 29 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19071 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 448371 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6133050 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 23 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 50083110 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 21 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 240997680 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 19 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 648149040 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 865196640 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 424116000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfi </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'> 3 </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'> 3 <sep /> 2 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 29469825 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -4096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 15 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 440320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 14 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 19310592 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 449691648 </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'> 6064521216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 48455497728 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 225104140800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 569506049280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 673428349440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 234654900480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 29331862560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8270262000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2432430000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 340540200 </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'> 58939650 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 29469825 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 29469825 </cn> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 31 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 432 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 29 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 19071 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 448371 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 25 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6133050 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 23 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 50083110 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 21 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 240997680 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 648149040 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 865196640 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 424116000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </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["3", ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["29469825", "-", RowBox[List["58939650", " ", "z"]], "+", RowBox[List["340540200", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2432430000", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["8270262000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["29331862560", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["234654900480", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["673428349440", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["569506049280", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["225104140800", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["48455497728", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["6064521216", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["449691648", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["19310592", " ", SuperscriptBox["z", "13"]]], "+", RowBox[List["440320", " ", SuperscriptBox["z", "14"]]], "-", RowBox[List["4096", " ", SuperscriptBox["z", "15"]]]]], "29469825"], "+", FractionBox[RowBox[List["1024", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "424116000"]], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["865196640", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "-", RowBox[List["648149040", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["240997680", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "-", RowBox[List["50083110", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "+", RowBox[List["6133050", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "-", RowBox[List["448371", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]], "+", RowBox[List["19071", " ", SuperscriptBox["z", RowBox[List["27", "/", "2"]]]]], "-", RowBox[List["432", " ", SuperscriptBox["z", RowBox[List["29", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["31", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]], "29469825"]]]]]]]










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





2007-05-02