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
Hypergeometric1F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1[a,b,z] > Specific values > For fixed z > For fixed z and a=-11/2





http://functions.wolfram.com/07.20.03.0172.01









  


  








Input Form





Hypergeometric1F1[-(11/2), 11/2, -z] == (1/(125829120 z^(9/2))) ((2 Sqrt[z] (-1091475 + 2 z (1195425 + 8 z (-239085 + 2 z (218295 + z (1042575 + 2 z (328155 + 4 z (19755 + z (2174 + z (109 + 2 z))))))))) + E^z Sqrt[Pi] (1091475 + 4 z (-779625 + z (1403325 + 8 z (-311850 + z (1091475 + 4 z (654885 + z (363825 + 2 z (41580 + z (4455 + 4 z (55 + z)))))))))) Erf[Sqrt[z]])/E^z)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric1F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", FractionBox["11", "2"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["125829120", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1091475"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1195425", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "239085"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["218295", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1042575", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["328155", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["19755", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2174", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["109", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["1091475", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "779625"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1403325", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "311850"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1091475", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["654885", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["363825", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["41580", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4455", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["55", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", 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> 1 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> <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;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;11&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;11&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[RowBox[List[&quot;-&quot;, &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> 125829120 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <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> 8 </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> <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> 4 </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> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 109 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2174 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 19755 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 328155 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1042575 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 218295 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 239085 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1195425 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1091475 </mn> </mrow> <mo> ) </mo> </mrow> </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> 4 </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> <mn> 4 </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> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 55 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 4455 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 41580 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 363825 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 654885 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1091475 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 311850 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1403325 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 779625 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1091475 </mn> </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> </mrow> <mo> ) </mo> </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'> 11 <sep /> 2 </cn> </apply> <cn type='rational'> 11 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 125829120 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <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'> 8 </cn> <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'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 109 </cn> </apply> </apply> <cn type='integer'> 2174 </cn> </apply> </apply> <cn type='integer'> 19755 </cn> </apply> </apply> <cn type='integer'> 328155 </cn> </apply> </apply> <cn type='integer'> 1042575 </cn> </apply> </apply> <cn type='integer'> 218295 </cn> </apply> </apply> <cn type='integer'> -239085 </cn> </apply> </apply> <cn type='integer'> 1195425 </cn> </apply> </apply> <cn type='integer'> -1091475 </cn> </apply> </apply> <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'> 4 </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 /> <cn type='integer'> 4 </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'> 4 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 55 </cn> </apply> </apply> <cn type='integer'> 4455 </cn> </apply> </apply> <cn type='integer'> 41580 </cn> </apply> </apply> <cn type='integer'> 363825 </cn> </apply> </apply> <cn type='integer'> 654885 </cn> </apply> </apply> <cn type='integer'> 1091475 </cn> </apply> </apply> <cn type='integer'> -311850 </cn> </apply> </apply> <cn type='integer'> 1403325 </cn> </apply> </apply> <cn type='integer'> -779625 </cn> </apply> </apply> <cn type='integer'> 1091475 </cn> </apply> <apply> <ci> Erf </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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["11", "2"]]], ",", FractionBox["11", "2"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1091475"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1195425", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "239085"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["218295", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1042575", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["328155", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["19755", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2174", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["109", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["1091475", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "779625"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1403325", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "311850"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1091475", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["654885", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["363825", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["41580", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["4455", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["55", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]]]], ")"]]]], RowBox[List["125829120", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]


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





2007-05-02