Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

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
Hypergeometric1F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1[a,b,z] > Specific values > For fixed z > For fixed z and a=-9/2





http://functions.wolfram.com/07.20.03.0196.01









  


  










Input Form





Hypergeometric1F1[-(9/2), 9/2, z] == (1/(1572864 z^(7/2))) (2 E^z Sqrt[z] (-14175 + 2 z (-17955 + 2 z (-19845 + 2 z (52827 + 2 z (-16077 + 2 z (1695 + 2 z (-71 + 2 z))))))) + Sqrt[Pi] (14175 - 16 z (-2835 + z (-6615 + 2 z (-13230 + z (33075 + 8 z (-2205 + z (441 + (-36 + z) z))))))) Erfi[Sqrt[z]])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric1F1", "[", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", FractionBox["9", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1572864", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "14175"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17955"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "19845"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["52827", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16077"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1695", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "71"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["14175", "-", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2835"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6615"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "13230"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["33075", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2205"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["441", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "36"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", 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> 1 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;1&quot;], SubscriptBox[&quot;F&quot;, &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;9&quot;, &quot;2&quot;]]], Hypergeometric1F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[FractionBox[&quot;9&quot;, &quot;2&quot;], Hypergeometric1F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, Hypergeometric1F1, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric1F1] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1572864 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 71 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1695 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 16077 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 52827 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 19845 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 17955 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 14175 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 14175 </mn> <mo> - </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 36 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 441 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2205 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 33075 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 13230 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 6615 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2835 </mn> </mrow> <mo> ) </mo> </mrow> </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> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric1F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <cn type='rational'> 9 <sep /> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1572864 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -71 </cn> </apply> </apply> <cn type='integer'> 1695 </cn> </apply> </apply> <cn type='integer'> -16077 </cn> </apply> </apply> <cn type='integer'> 52827 </cn> </apply> </apply> <cn type='integer'> -19845 </cn> </apply> </apply> <cn type='integer'> -17955 </cn> </apply> </apply> <cn type='integer'> -14175 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 14175 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -36 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 441 </cn> </apply> </apply> <cn type='integer'> -2205 </cn> </apply> </apply> <cn type='integer'> 33075 </cn> </apply> </apply> <cn type='integer'> -13230 </cn> </apply> </apply> <cn type='integer'> -6615 </cn> </apply> </apply> <cn type='integer'> -2835 </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["Hypergeometric1F1", "[", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", FractionBox["9", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "14175"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17955"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "19845"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["52827", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16077"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1695", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "71"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["14175", "-", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2835"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6615"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "13230"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["33075", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2205"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["441", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "36"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["1572864", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]]]]]










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





2007-05-02





© 1998- Wolfram Research, Inc.