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 | | http://functions.wolfram.com/07.25.03.a7zy.01 | 
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 | | HypergeometricPFQ[{-(5/2), 4}, {2, 11/2}, z] == 
 (9 E^z (-2625 + 700 z + 420 z^2 - 1760 z^3 + 16208 z^4 - 7488 z^5 + 
     704 z^6))/(262144 z^4) - (1/(524288 z^(9/2))) 
   (9 Sqrt[Pi] (-2625 - 1050 z + 420 z^2 - 1400 z^3 - 14000 z^4 + 39200 z^5 - 
     15680 z^6 + 1408 z^7) Erfi[Sqrt[z]]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", FractionBox["11", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["9", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2625"]], "+", RowBox[List["700", " ", "z"]], "+", RowBox[List["420", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1760", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["16208", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["7488", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["704", " ", SuperscriptBox["z", "6"]]]]], ")"]]]], RowBox[List["262144", " ", SuperscriptBox["z", "4"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["524288", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["9", " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2625"]], "-", RowBox[List["1050", " ", "z"]], "+", RowBox[List["420", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1400", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["14000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["39200", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["15680", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1408", " ", SuperscriptBox["z", "7"]]]]], ")"]], " ", RowBox[List["Erfi", "[", 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>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 5 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mn> 4 </mn>  </mrow>  <mo> ; </mo>  <mrow>  <mn> 2 </mn>  <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[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["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>  <mfrac>  <mrow>  <mn> 9 </mn>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mi> z </mi>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 704 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 7488 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 16208 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 1760 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 420 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 700 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 2625 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 262144 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  </mfrac>  <mo> - </mo>  <mfrac>  <mrow>  <mn> 9 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 1408 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 15680 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 39200 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 14000 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 1400 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 420 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 1050 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 2625 </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>  <mn> 524288 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 9 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  <cn type='integer'> 4 </cn>  </list>  <list>  <cn type='integer'> 2 </cn>  <cn type='rational'> 11 <sep /> 2 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 9 </cn>  <apply>  <power />  <exponentiale />  <ci> z </ci>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 704 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 7488 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 16208 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 1760 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 420 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 700 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -2625 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 262144 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 9 </cn>  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 1408 </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'> 15680 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 39200 </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'> 14000 </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'> 1400 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 420 </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'> 1050 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> -2625 </cn>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 524288 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 9 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </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[RowBox[List["-", FractionBox["5", "2"]]], ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", FractionBox["11", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["9", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2625"]], "+", RowBox[List["700", " ", "z"]], "+", RowBox[List["420", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1760", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["16208", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["7488", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["704", " ", SuperscriptBox["z", "6"]]]]], ")"]]]], RowBox[List["262144", " ", SuperscriptBox["z", "4"]]]], "-", FractionBox[RowBox[List["9", " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2625"]], "-", RowBox[List["1050", " ", "z"]], "+", RowBox[List["420", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1400", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["14000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["39200", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["15680", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1408", " ", SuperscriptBox["z", "7"]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]], RowBox[List["524288", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]]] | 
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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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