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 | | http://functions.wolfram.com/07.25.03.4918.01 | 
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 | | HypergeometricPFQ[{-(9/2), 4}, {3, 3}, z] == 
 -((1/135135) (2 E^(z/2) (-67725 + 166950 z - 124356 z^2 + 36000 z^3 - 
      4176 z^4 + 160 z^5) BesselI[0, z/2])) + 
  (1/(135135 z)) (2 E^(z/2) (-630 - 7875 z + 85326 z^2 - 94140 z^3 + 
     32064 z^4 - 4016 z^5 + 160 z^6) BesselI[1, z/2]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List["3", ",", "3"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", "135135"], RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "67725"]], "+", RowBox[List["166950", " ", "z"]], "-", RowBox[List["124356", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["36000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["4176", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]]]]]], "+", RowBox[List[FractionBox["1", RowBox[List["135135", " ", "z"]]], RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "630"]], "-", RowBox[List["7875", " ", "z"]], "+", RowBox[List["85326", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["94140", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["32064", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["4016", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]]]]]]]]]] | 
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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> 9 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mn> 4 </mn>  </mrow>  <mo> ; </mo>  <mrow>  <mn> 3 </mn>  <mo> , </mo>  <mn> 3 </mn>  </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["9", "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["3", 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["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> 2 </mn>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mi> z </mi>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 160 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 4016 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 32064 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 94140 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 85326 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 7875 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 630 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> I </mi>  <mn> 1 </mn>  </msub>  <mo> ( </mo>  <mfrac>  <mi> z </mi>  <mn> 2 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 135135 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  <mo> - </mo>  <mfrac>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mi> z </mi>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 160 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 4176 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 36000 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 124356 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 166950 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 67725 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> I </mi>  <mn> 0 </mn>  </msub>  <mo> ( </mo>  <mfrac>  <mi> z </mi>  <mn> 2 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  <mn> 135135 </mn>  </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'> 9 <sep /> 2 </cn>  </apply>  <cn type='integer'> 4 </cn>  </list>  <list>  <cn type='integer'> 3 </cn>  <cn type='integer'> 3 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <exponentiale />  <apply>  <times />  <ci> z </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 160 </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'> 4016 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 32064 </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'> 94140 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 85326 </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'> 7875 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> -630 </cn>  </apply>  <apply>  <ci> BesselI </ci>  <cn type='integer'> 1 </cn>  <apply>  <times />  <ci> z </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 135135 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <exponentiale />  <apply>  <times />  <ci> z </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 160 </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'> 4176 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 36000 </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'> 124356 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 166950 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -67725 </cn>  </apply>  <apply>  <ci> BesselI </ci>  <cn type='integer'> 0 </cn>  <apply>  <times />  <ci> z </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <cn type='integer'> 135135 </cn>  <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["9", "2"]]], ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List["3", ",", "3"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "67725"]], "+", RowBox[List["166950", " ", "z"]], "-", RowBox[List["124356", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["36000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["4176", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "135135"]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "630"]], "-", RowBox[List["7875", " ", "z"]], "+", RowBox[List["85326", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["94140", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["32064", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["4016", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]], RowBox[List["135135", " ", "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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