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 | | http://functions.wolfram.com/07.25.03.ai31.01 | 
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 | | HypergeometricPFQ[{2, 9/2}, {-(11/2), -(1/2)}, z] == 
 (1/1091475) (1091475 + 3572100 z - 13097700 z^2 + 21621600 z^3 - 
    32432400 z^4 + 63011520 z^5 - 310390080 z^6 - 425456640 z^7 - 
    176682240 z^8 - 32680960 z^9 - 2958336 z^10 - 126976 z^11 - 2048 z^12) - 
  (1/1091475) (1024 E^z Sqrt[Pi] (453600 z^(13/2) + 488880 z^(15/2) + 
     187200 z^(17/2) + 33300 z^(19/2) + 2950 z^(21/2) + 125 z^(23/2) + 
     2 z^(25/2)) Erf[Sqrt[z]]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["2", ",", FractionBox["9", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "1091475"], RowBox[List["(", RowBox[List["1091475", "+", RowBox[List["3572100", " ", "z"]], "-", RowBox[List["13097700", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["21621600", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["32432400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["63011520", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["310390080", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["425456640", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["176682240", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["32680960", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["2958336", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["126976", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["2048", " ", SuperscriptBox["z", "12"]]]]], ")"]]]], "-", RowBox[List[FractionBox["1", "1091475"], RowBox[List["(", RowBox[List["1024", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["453600", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["488880", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["187200", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["33300", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["2950", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "+", RowBox[List["125", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "+", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]]]], ")"]], " ", 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> 2 </mn>  <mo> , </mo>  <mfrac>  <mn> 9 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 11 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  </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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "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["11", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "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> 1091475 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 2048 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 12 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 126976 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 11 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2958336 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 10 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 32680960 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 9 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 176682240 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 425456640 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 310390080 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 63011520 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 32432400 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 21621600 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 13097700 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 3572100 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 1091475 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 1091475 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mn> 1024 </mn>  <mo> ⁢ </mo>  <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>  <msup>  <mi> z </mi>  <mrow>  <mn> 25 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 125 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 23 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2950 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 21 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 33300 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 19 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 187200 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 17 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 488880 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 15 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 453600 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 13 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  </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>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='integer'> 2 </cn>  <cn type='rational'> 9 <sep /> 2 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 11 <sep /> 2 </cn>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='rational'> 1 <sep /> 1091475 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -2048 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 12 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 126976 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 11 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2958336 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 10 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 32680960 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 9 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 176682240 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 425456640 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 310390080 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 63011520 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 32432400 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 21621600 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 13097700 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 3572100 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 1091475 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='rational'> 1 <sep /> 1091475 </cn>  <apply>  <times />  <cn type='integer'> 1024 </cn>  <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>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 25 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 125 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 23 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2950 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 21 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 33300 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 19 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 187200 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 17 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 488880 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 15 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 453600 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 13 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Erf </ci>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </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["{", RowBox[List["2", ",", FractionBox["9", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["1091475", "+", RowBox[List["3572100", " ", "z"]], "-", RowBox[List["13097700", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["21621600", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["32432400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["63011520", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["310390080", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["425456640", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["176682240", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["32680960", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["2958336", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["126976", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["2048", " ", SuperscriptBox["z", "12"]]]]], "1091475"], "-", FractionBox[RowBox[List["1024", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["453600", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["488880", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["187200", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["33300", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["2950", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "+", RowBox[List["125", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "+", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], "1091475"]]]]]]] | 
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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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