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
Hypergeometric1F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1Regularized[a,b,z] > Specific values > For fixed z > For fixed z and a=11/2





http://functions.wolfram.com/07.21.03.0549.01









  


  








Input Form





Hypergeometric1F1Regularized[11/2, -3, z] == (1/3780) (E^(z/2) z (z (2835 + z (-6615 + 8 z (46305 + z (59535 + 2 z (12315 + z (2121 + 4 z (39 + z))))))) BesselI[0, z/2] + (-11340 + z (26460 + z (-46305 + 8 z (13230 + z (40395 + 2 z (10416 + z (1971 + 4 z (38 + z)))))))) BesselI[1, z/2]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[FractionBox["11", "2"], ",", RowBox[List["-", "3"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "3780"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List["2835", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6615"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["46305", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["59535", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["12315", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2121", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["39", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "11340"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["26460", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "46305"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["13230", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["40395", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["10416", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1971", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["38", "+", "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> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mn> 3 </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;1&quot;], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[TagBox[FractionBox[&quot;11&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[RowBox[List[&quot;-&quot;, &quot;3&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> 3780 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> z </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <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> 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> 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> 39 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2121 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 12315 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 59535 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 46305 </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> <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> <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> 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> 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> 38 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1971 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 10416 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 40395 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 13230 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 46305 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 26460 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 11340 </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> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric1F1Regularized </ci> <cn type='rational'> 11 <sep /> 2 </cn> <cn type='integer'> -3 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 3780 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> z </ci> <apply> <plus /> <apply> <times /> <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'> 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'> 39 </cn> </apply> </apply> <cn type='integer'> 2121 </cn> </apply> </apply> <cn type='integer'> 12315 </cn> </apply> </apply> <cn type='integer'> 59535 </cn> </apply> </apply> <cn type='integer'> 46305 </cn> </apply> </apply> <cn type='integer'> -6615 </cn> </apply> </apply> <cn type='integer'> 2835 </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 /> <apply> <plus /> <apply> <times /> <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'> 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'> 38 </cn> </apply> </apply> <cn type='integer'> 1971 </cn> </apply> </apply> <cn type='integer'> 10416 </cn> </apply> </apply> <cn type='integer'> 40395 </cn> </apply> </apply> <cn type='integer'> 13230 </cn> </apply> </apply> <cn type='integer'> -46305 </cn> </apply> </apply> <cn type='integer'> 26460 </cn> </apply> </apply> <cn type='integer'> -11340 </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> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[FractionBox["11", "2"], ",", RowBox[List["-", "3"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List["2835", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6615"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["46305", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["59535", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["12315", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2121", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["39", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "11340"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["26460", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "46305"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["13230", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["40395", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["10416", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1971", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["38", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]]]], ")"]]]], "3780"]]]]]


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





2007-05-02