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http://functions.wolfram.com/07.21.03.0545.01
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Hypergeometric1F1Regularized[11/2, -5, z] ==
(1/7560) (E^(z/2) z
(8 z (14175 + z (-22680 +
z (22680 + z (-19845 + 2 z (158760 + z (155925 + 4 z (12264 +
z (1641 + 2 z (48 + z))))))))) BesselI[0, z/2] +
(-453600 + z (725760 + z (-739935 + 8 z (82215 +
2 z (-39690 + z (59535 + 2 z (57813 + 2 z (10761 +
2 z (774 + z (47 + z)))))))))) BesselI[1, z/2]))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[FractionBox["11", "2"], ",", RowBox[List["-", "5"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "7560"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["14175", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "22680"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["22680", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "19845"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["158760", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["155925", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["12264", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1641", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["48", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "453600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["725760", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "739935"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["82215", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "39690"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["59535", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["57813", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["10761", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["774", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["47", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]
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<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>   </mo> <mn> 1 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox[OverscriptBox["F", "~"], "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[FractionBox["11", "2"], Hypergeometric1F1Regularized, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", "5"]], Hypergeometric1F1Regularized, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", Hypergeometric1F1Regularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric1F1Regularized] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 7560 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> z </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 48 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1641 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 12264 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 155925 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 158760 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 19845 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 22680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 22680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 14175 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </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> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 47 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 774 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 10761 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 57813 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 59535 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 39690 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 82215 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 739935 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 725760 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 453600 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </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'> -5 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 7560 </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 /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <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> <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 /> <ci> z </ci> <cn type='integer'> 48 </cn> </apply> </apply> <cn type='integer'> 1641 </cn> </apply> </apply> <cn type='integer'> 12264 </cn> </apply> </apply> <cn type='integer'> 155925 </cn> </apply> </apply> <cn type='integer'> 158760 </cn> </apply> </apply> <cn type='integer'> -19845 </cn> </apply> </apply> <cn type='integer'> 22680 </cn> </apply> </apply> <cn type='integer'> -22680 </cn> </apply> </apply> <cn type='integer'> 14175 </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 /> <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'> 2 </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 /> <ci> z </ci> <cn type='integer'> 47 </cn> </apply> </apply> <cn type='integer'> 774 </cn> </apply> </apply> <cn type='integer'> 10761 </cn> </apply> </apply> <cn type='integer'> 57813 </cn> </apply> </apply> <cn type='integer'> 59535 </cn> </apply> </apply> <cn type='integer'> -39690 </cn> </apply> </apply> <cn type='integer'> 82215 </cn> </apply> </apply> <cn type='integer'> -739935 </cn> </apply> </apply> <cn type='integer'> 725760 </cn> </apply> </apply> <cn type='integer'> -453600 </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>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[FractionBox["11", "2"], ",", RowBox[List["-", "5"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["14175", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "22680"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["22680", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "19845"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["158760", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["155925", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["12264", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1641", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["48", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "453600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["725760", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "739935"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["82215", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "39690"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["59535", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["57813", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["10761", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["774", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["47", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]]]], ")"]]]], "7560"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQRegularized[{},{b},z] | HypergeometricPFQRegularized[{a1,a2},{b1},z] | HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] | |
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