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http://functions.wolfram.com/07.20.03.0507.01
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Hypergeometric1F1[6, -(9/2), z] ==
(1/113400)
(-2 (-56700 +
z (75600 + z (-75600 + z (80640 + z (-120960 +
z (483840 + z (451395 + 8 z (16035 + 2 z (972 + z (52 +
z)))))))))) - E^z Sqrt[Pi] z^(11/2)
(1322685 + 2 z (508725 + 4 z (33915 + 2 z (1995 + z (105 + 2 z)))))
Erf[Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric1F1", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "113400"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "56700"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["75600", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "75600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["80640", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "120960"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["483840", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["451395", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["16035", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["972", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["52", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1322685", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["508725", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["33915", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1995", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["105", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]]]], ")"]]]]]]]]
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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> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox["6", Hypergeometric1F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["9", "2"]]], Hypergeometric1F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", Hypergeometric1F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric1F1] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 113400 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> </mrow> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <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> <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> </mrow> <mo> + </mo> <mn> 105 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1995 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 33915 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 508725 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1322685 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <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> <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> 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> <mi> z </mi> <mo> + </mo> <mn> 52 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 972 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 16035 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 451395 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 483840 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 120960 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 80640 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 75600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 75600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 56700 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric1F1 </ci> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 113400 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <power /> <pi /> <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'> 4 </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> <cn type='integer'> 105 </cn> </apply> </apply> <cn type='integer'> 1995 </cn> </apply> </apply> <cn type='integer'> 33915 </cn> </apply> </apply> <cn type='integer'> 508725 </cn> </apply> </apply> <cn type='integer'> 1322685 </cn> </apply> <apply> <ci> Erf </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <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 /> <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 /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 52 </cn> </apply> </apply> <cn type='integer'> 972 </cn> </apply> </apply> <cn type='integer'> 16035 </cn> </apply> </apply> <cn type='integer'> 451395 </cn> </apply> </apply> <cn type='integer'> 483840 </cn> </apply> </apply> <cn type='integer'> -120960 </cn> </apply> </apply> <cn type='integer'> 80640 </cn> </apply> </apply> <cn type='integer'> -75600 </cn> </apply> </apply> <cn type='integer'> 75600 </cn> </apply> </apply> <cn type='integer'> -56700 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric1F1", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "56700"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["75600", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "75600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["80640", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "120960"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["483840", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["451395", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["16035", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["972", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["52", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1322685", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["508725", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["33915", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1995", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["105", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]]]], "113400"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
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