|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.32.03.0116.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricPFQRegularized[{}, {1, 5/2, 5/2}, z] ==
(1/(8 Pi z^(3/2))) (BesselI[0, 4 z^(1/4)] - BesselJ[0, 4 z^(1/4)] +
4 Sqrt[z] (BesselI[0, 4 z^(1/4)] + BesselJ[0, 4 z^(1/4)]) -
4 z^(1/4) (BesselI[1, 4 z^(1/4)] + BesselJ[1, 4 z^(1/4)]))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", FractionBox["5", "2"], ",", FractionBox["5", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["8", " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["0", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]], "-", RowBox[List["BesselJ", "[", RowBox[List["0", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]], "+", RowBox[List["4", " ", SqrtBox["z"], RowBox[List["(", " ", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["0", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]], "+", " ", RowBox[List["BesselJ", "[", RowBox[List["0", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["1", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]], "+", RowBox[List["BesselJ", "[", RowBox[List["1", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]]]], ")"]]]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> 0 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 3 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mo>   </mo> <mo> ; </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </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]", FormBox["0", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> J </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> J </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msub> <mi> J </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQRegularized </ci> <list /> <list> <cn type='integer'> 1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <ci> BesselJ </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <ci> BesselJ </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> BesselJ </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", FractionBox["5", "2"], ",", FractionBox["5", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["BesselI", "[", RowBox[List["0", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]], "-", RowBox[List["BesselJ", "[", RowBox[List["0", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]], "+", RowBox[List["4", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["0", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]], "+", RowBox[List["BesselJ", "[", RowBox[List["0", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["1", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]], "+", RowBox[List["BesselJ", "[", RowBox[List["1", ",", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]]]], ")"]]]]]], RowBox[List["8", " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|