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http://functions.wolfram.com/07.21.03.0568.01
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Hypergeometric1F1Regularized[6, -(11/2), z] ==
(1/(3840 Sqrt[Pi]))
(2 (311850 + z (-340200 +
z (264600 + z (-201600 + z (181440 + z (-241920 + z (887040 +
z (701145 + 4 z (43635 + 2 z (2359 + 2 z (57 +
z))))))))))) + E^z Sqrt[Pi] z^(13/2)
(2340135 + 2 z (780045 + 4 z (45885 + 2 z (2415 + z (115 + 2 z)))))
Erf[Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["3840", " ", SqrtBox["\[Pi]"]]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["311850", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "340200"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["264600", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "201600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["181440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "241920"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["887040", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["701145", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["43635", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2359", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["57", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2340135", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["780045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["45885", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["115", "+", 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> 11 </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["11", "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> 115 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2415 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45885 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 780045 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2340135 </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> 13 </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> <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> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 57 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2359 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 43635 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 701145 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 887040 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 241920 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 181440 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 201600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 264600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 340200 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 311850 </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'> 11 <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'> 115 </cn> </apply> </apply> <cn type='integer'> 2415 </cn> </apply> </apply> <cn type='integer'> 45885 </cn> </apply> </apply> <cn type='integer'> 780045 </cn> </apply> </apply> <cn type='integer'> 2340135 </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'> 13 <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 /> <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'> 4 </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 /> <ci> z </ci> <cn type='integer'> 57 </cn> </apply> </apply> <cn type='integer'> 2359 </cn> </apply> </apply> <cn type='integer'> 43635 </cn> </apply> </apply> <cn type='integer'> 701145 </cn> </apply> </apply> <cn type='integer'> 887040 </cn> </apply> </apply> <cn type='integer'> -241920 </cn> </apply> </apply> <cn type='integer'> 181440 </cn> </apply> </apply> <cn type='integer'> -201600 </cn> </apply> </apply> <cn type='integer'> 264600 </cn> </apply> </apply> <cn type='integer'> -340200 </cn> </apply> </apply> <cn type='integer'> 311850 </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["11", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["311850", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "340200"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["264600", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "201600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["181440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "241920"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["887040", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["701145", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["43635", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2359", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["57", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2340135", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["780045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["45885", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["115", "+", 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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