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 | | http://functions.wolfram.com/07.22.03.6418.01 | 
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 | | HypergeometricPFQ[{1}, {-(1/4), 9/4}, z] == 
 -((1/(32 z^(5/4))) ((5 (-24 E^(2 Sqrt[z]) z^(1/4) + E^(4 Sqrt[z]) Sqrt[2 Pi] 
       (3 - 6 Sqrt[z] + 4 z) Erf[Sqrt[2] z^(1/4)] + 
      Sqrt[2 Pi] (3 + 6 Sqrt[z] + 4 z) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], ",", FractionBox["9", "4"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "4"]]]]]], RowBox[List["(", RowBox[List["5", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "24"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["6", " ", SqrtBox["z"]]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["6", " ", SqrtBox["z"]]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]]] | 
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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> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> ; </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mfrac>  <mn> 9 </mn>  <mn> 4 </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", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["1", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation>  </semantics>  <mo>  </mo>  <mrow>  <mo> - </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 32 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 4 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 5 </mn>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mrow>  <mo> - </mo>  <mn> 2 </mn>  </mrow>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  </msup>  <mo> ⁢ </mo>  <msqrt>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> π </mi>  </mrow>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mrow>  <mn> 6 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> + </mo>  <mn> 3 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> erf </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msqrt>  <mn> 2 </mn>  </msqrt>  <mo> ⁢ </mo>  <mroot>  <mi> z </mi>  <mn> 4 </mn>  </mroot>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <msqrt>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> π </mi>  </mrow>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mn> 6 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> + </mo>  <mn> 3 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msqrt>  <mn> 2 </mn>  </msqrt>  <mo> ⁢ </mo>  <mroot>  <mi> z </mi>  <mn> 4 </mn>  </mroot>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <mn> 24 </mn>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  </msup>  <mo> ⁢ </mo>  <mroot>  <mi> z </mi>  <mn> 4 </mn>  </mroot>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='integer'> 1 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  <cn type='rational'> 9 <sep /> 4 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 32 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 4 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 5 </cn>  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -2 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <pi />  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 6 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> 3 </cn>  </apply>  <apply>  <ci> Erf </ci>  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <pi />  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> 6 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> 3 </cn>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 24 </cn>  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 4 </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["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], ",", FractionBox["9", "4"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["5", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "24"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["6", " ", SqrtBox["z"]]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["6", " ", SqrtBox["z"]]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "4"]]]]]]]]]]]] | 
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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[{a},{b},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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