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http://functions.wolfram.com/07.21.03.0583.01
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Hypergeometric1F1Regularized[6, -(1/2), z] ==
(1/(3840 Sqrt[Pi]))
(2 (-960 + z (11520 + z (35595 + 8 z (2905 + 2 z (342 + z (32 + z)))))) +
E^z Sqrt[Pi] z^(3/2) (45045 +
2 z (45045 + 4 z (6435 + 2 z (715 + z (65 + 2 z))))) Erf[Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["3840", " ", SqrtBox["\[Pi]"]]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "960"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11520", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["35595", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["2905", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["342", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["32", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["45045", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["45045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["6435", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["715", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["65", "+", 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> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </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[OverscriptBox["F", "~"], "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox["6", Hypergeometric1F1Regularized, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["1", "2"]]], 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> <mrow> <mn> 3840 </mn> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <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> 65 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 715 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6435 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45045 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45045 </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> 3 </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> <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> 32 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 342 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2905 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 35595 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 11520 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 960 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric1F1Regularized </ci> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3840 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <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'> 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'> 65 </cn> </apply> </apply> <cn type='integer'> 715 </cn> </apply> </apply> <cn type='integer'> 6435 </cn> </apply> </apply> <cn type='integer'> 45045 </cn> </apply> </apply> <cn type='integer'> 45045 </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'> 3 <sep /> 2 </cn> </apply> </apply> <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 /> <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'> 32 </cn> </apply> </apply> <cn type='integer'> 342 </cn> </apply> </apply> <cn type='integer'> 2905 </cn> </apply> </apply> <cn type='integer'> 35595 </cn> </apply> </apply> <cn type='integer'> 11520 </cn> </apply> </apply> <cn type='integer'> -960 </cn> </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["6", ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "960"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11520", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["35595", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["2905", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["342", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["32", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["45045", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["45045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["6435", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["715", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["65", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["3840", " ", SqrtBox["\[Pi]"]]]]]]]] |
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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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