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http://functions.wolfram.com/07.21.03.0059.01
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Hypergeometric1F1Regularized[3/2, 7/2, z] ==
(6 E^z Sqrt[z] - Sqrt[Pi] (3 + 2 z) Erfi[Sqrt[z]])/(2 Sqrt[Pi] z^(5/2))
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Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["6", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["z"]]], "-", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "z"]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["5", "/", "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> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[FractionBox["3", "2"], Hypergeometric1F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["7", "2"], Hypergeometric1F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False]], ";", TagBox["z", Hypergeometric1F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric1F1Regularized] </annotation> </semantics> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mrow> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric1F1Regularized </ci> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["6", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["z"]]], "-", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "z"]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]] |
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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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