|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.25.03.3970.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricPFQ[{-(9/2), 3/2}, {3/2, 2}, z] ==
(E^(z/2) (10395 - 28350 z + 22524 z^2 - 6816 z^3 + 816 z^4 - 32 z^5)
BesselI[0, z/2])/10395 +
(E^(z/2) (-945 + 13854 z - 16836 z^2 + 6048 z^3 - 784 z^4 + 32 z^5)
BesselI[1, z/2])/10395
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "2"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List["10395", "-", RowBox[List["28350", " ", "z"]], "+", RowBox[List["22524", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["6816", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["816", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["32", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "10395"], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "945"]], "+", RowBox[List["13854", " ", "z"]], "-", RowBox[List["16836", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["6048", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["784", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]], "10395"]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 2 </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[FractionBox["3", "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[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["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> <msup> <mi> ⅇ </mi> <mrow> <mi> z </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 32 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 816 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6816 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 22524 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 28350 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 10395 </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> 10395 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> z </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 32 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 784 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6048 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16836 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13854 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 945 </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> <mn> 10395 </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='rational'> 3 <sep /> 2 </cn> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='integer'> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <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'> -32 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 816 </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'> 6816 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 22524 </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'> 28350 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 10395 </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'> 10395 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <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'> 32 </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'> 784 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6048 </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'> 16836 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 13854 </cn> <ci> z </ci> </apply> <cn type='integer'> -945 </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 /> <cn type='integer'> 10395 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "2"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List["10395", "-", RowBox[List["28350", " ", "z"]], "+", RowBox[List["22524", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["6816", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["816", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["32", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "10395"], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "945"]], "+", RowBox[List["13854", " ", "z"]], "-", RowBox[List["16836", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["6048", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["784", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]], "10395"]]]]]]] |
|
|
|
|
|
|
|
|
|
|
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] | |
|
|
|