| |  
 |  | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | http://functions.wolfram.com/07.25.03.agcg.01 | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | HypergeometricPFQ[{3/2, 3}, {-(11/2), -(5/2)}, -z] == 
 (1/155925) (155925 - 51030 z + 37800 z^2 - 126000 z^3 - 680400 z^4 - 
    2328480 z^5 - 16144128 z^6 + 34122240 z^7 - 19388160 z^8 + 4623872 z^9 - 
    519168 z^10 + 26880 z^11 - 512 z^12) + 
  (1/155925) ((128 Sqrt[Pi] (214200 z^(13/2) - 328440 z^(15/2) + 
      167748 z^(17/2) - 38052 z^(19/2) + 4159 z^(21/2) - 212 z^(23/2) + 
      4 z^(25/2)) Erfi[Sqrt[z]])/E^z) | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "155925"], RowBox[List["(", RowBox[List["155925", "-", RowBox[List["51030", " ", "z"]], "+", RowBox[List["37800", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["126000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["680400", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2328480", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["16144128", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["34122240", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["19388160", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["4623872", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["519168", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["26880", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["512", " ", SuperscriptBox["z", "12"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "155925"], RowBox[List["(", RowBox[List["128", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["214200", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "-", RowBox[List["328440", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["167748", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "-", RowBox[List["38052", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["4159", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "-", RowBox[List["212", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]], ")"]]]]]]]]]] | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 | | 
   <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>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mn> 3 </mn>  </mrow>  <mo> ; </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 11 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 5 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </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[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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> 155925 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 512 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 12 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 26880 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 11 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 519168 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 10 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 4623872 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 9 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 19388160 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 34122240 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 16144128 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2328480 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 680400 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 126000 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 37800 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 51030 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 155925 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 155925 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mn> 128 </mn>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 25 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 212 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 23 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 4159 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 21 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 38052 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 19 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 167748 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 17 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 328440 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 15 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 214200 </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> erfi </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='rational'> 3 <sep /> 2 </cn>  <cn type='integer'> 3 </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'> 5 <sep /> 2 </cn>  </apply>  </list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='rational'> 1 <sep /> 155925 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -512 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 12 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 26880 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 11 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 519168 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 10 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 4623872 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 9 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 19388160 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 34122240 </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'> 16144128 </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'> 2328480 </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'> 680400 </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'> 126000 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 37800 </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'> 51030 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 155925 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 155925 </cn>  <apply>  <times />  <cn type='integer'> 128 </cn>  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 25 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 212 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 23 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 4159 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 21 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 38052 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 19 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 167748 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 17 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 328440 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 15 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 214200 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 13 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["155925", "-", RowBox[List["51030", " ", "z"]], "+", RowBox[List["37800", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["126000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["680400", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2328480", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["16144128", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["34122240", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["19388160", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["4623872", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["519168", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["26880", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["512", " ", SuperscriptBox["z", "12"]]]]], "155925"], "+", FractionBox[RowBox[List["128", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["214200", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "-", RowBox[List["328440", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["167748", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "-", RowBox[List["38052", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["4159", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "-", RowBox[List["212", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]], "155925"]]]]]]] | 
 |  
 |   
 |  
 |  
 | |   
 |  
 |  
 |  
 |  
 |  
 |  
 | | Date Added to functions.wolfram.com (modification date) | 
 |  
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |   
 |  
 |  
 |  |  | 
 | | 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] |  |  | 
 | 
 
 | 
 |