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 | | http://functions.wolfram.com/07.25.03.anel.01 | 
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 | | HypergeometricPFQ[{5, 11/2}, {-(5/2), 11/2}, z] == 
 (1/360) (360 - 720 z + 1440 z^2 - 6720 z^3 - 7575 z^4 - 2226 z^5 - 236 z^6 - 
    8 z^7) - (1/720) E^z Sqrt[Pi] z^(7/2) (19305 + 17160 z + 4680 z^2 + 
    480 z^3 + 16 z^4) Erf[Sqrt[z]] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["5", ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", FractionBox["11", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "360"], " ", RowBox[List["(", RowBox[List["360", "-", RowBox[List["720", " ", "z"]], "+", RowBox[List["1440", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["6720", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["7575", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2226", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["236", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["8", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "-", RowBox[List[FractionBox["1", "720"], " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["19305", "+", RowBox[List["17160", " ", "z"]], "+", RowBox[List["4680", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["480", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["16", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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> 2 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 5 </mn>  <mo> , </mo>  <mfrac>  <mn> 11 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 5 </mn>  <mn> 2 </mn>  </mfrac>  </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]", "2"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "2"], 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["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "2"], 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>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 360 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 8 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 236 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2226 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 7575 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 6720 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1440 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 720 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 360 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 720 </mn>  </mfrac>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mi> z </mi>  </msup>  <mo> ⁢ </mo>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 16 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 480 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 4680 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 17160 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 19305 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> erf </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='integer'> 5 </cn>  <cn type='rational'> 11 <sep /> 2 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  <cn type='rational'> 11 <sep /> 2 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='rational'> 1 <sep /> 360 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -8 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 236 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2226 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 7575 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 6720 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1440 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 720 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 360 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='rational'> 1 <sep /> 720 </cn>  <apply>  <power />  <exponentiale />  <ci> z </ci>  </apply>  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 16 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 480 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 4680 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 17160 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 19305 </cn>  </apply>  <apply>  <ci> Erf </ci>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </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["{", RowBox[List["5", ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", FractionBox["11", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "360"], " ", RowBox[List["(", RowBox[List["360", "-", RowBox[List["720", " ", "z"]], "+", RowBox[List["1440", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["6720", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["7575", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2226", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["236", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["8", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "-", RowBox[List[FractionBox["1", "720"], " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["19305", "+", RowBox[List["17160", " ", "z"]], "+", RowBox[List["4680", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["480", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["16", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]]]]]]]] | 
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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},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1},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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