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
Hypergeometric1F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1Regularized[a,b,z] > Specific values > For fixed z > For fixed z and a=-9/2





http://functions.wolfram.com/07.21.03.0159.01









  


  










Input Form





Hypergeometric1F1Regularized[-(9/2), 1, z] == (1/945) E^(z/2) ((945 + z (-4725 + 4 z (1371 + z (-555 - 4 (-21 + z) z)))) BesselI[0, z/2] + z (1689 + 4 z (-930 + z (477 + 4 (-20 + z) z))) BesselI[1, z/2])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", "1", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "945"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["945", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4725"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1371", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "555"]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1689", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "930"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["477", "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "20"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]]]], ")"]]]]]]]]










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> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <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> <mn> 1 </mn> <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[OverscriptBox[&quot;F&quot;, &quot;~&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;]]], Hypergeometric1F1Regularized, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[&quot;1&quot;, Hypergeometric1F1Regularized, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, Hypergeometric1F1Regularized, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric1F1Regularized] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 945 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> z </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <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> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 21 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 555 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1371 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 4725 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 945 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <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> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 20 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 477 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 930 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1689 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric1F1Regularized </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 945 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <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'> -4 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -21 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -555 </cn> </apply> </apply> <cn type='integer'> 1371 </cn> </apply> </apply> <cn type='integer'> -4725 </cn> </apply> </apply> <cn type='integer'> 945 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <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'> 4 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -20 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 477 </cn> </apply> </apply> <cn type='integer'> -930 </cn> </apply> </apply> <cn type='integer'> 1689 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", "1", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "945"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["945", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4725"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1371", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "555"]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1689", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "930"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["477", "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "20"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]]]], ")"]]]]]]]]










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





2007-05-02





© 1998- Wolfram Research, Inc.