|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.22.03.1671.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricPFQ[{-(5/2)}, {5, 5}, z] ==
-((1/(2029052025 z^(7/2)))
(512 (2 Sqrt[z] (-6081075 - 9258030 z - 5143860 z^2 - 4582800 z^3 +
1247040 z^4 - 54272 z^5 + 512 z^6) BesselI[0, Sqrt[z]]^2 +
(24324300 + 27442665 z + 13922460 z^2 + 7467840 z^3 - 2414400 z^4 +
107776 z^5 - 1024 z^6) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] +
Sqrt[z] (25259985 + 25468110 z + 13305960 z^2 + 7996800 z^3 -
2440576 z^4 + 108032 z^5 - 1024 z^6) BesselI[1, Sqrt[z]]^2)))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["5", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["5", ",", "5"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["2029052025", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]], RowBox[List["(", RowBox[List["512", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6081075"]], "-", RowBox[List["9258030", " ", "z"]], "-", RowBox[List["5143860", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4582800", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1247040", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["54272", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["512", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List["0", ",", SqrtBox["z"]]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["24324300", "+", RowBox[List["27442665", " ", "z"]], "+", RowBox[List["13922460", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7467840", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2414400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["107776", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["1024", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", SqrtBox["z"]]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", SqrtBox["z"]]], "]"]]]], "+", RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List["25259985", "+", RowBox[List["25468110", " ", "z"]], "+", RowBox[List["13305960", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7996800", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2440576", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["108032", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["1024", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List["1", ",", SqrtBox["z"]]], "]"]], "2"]]]]], ")"]]]], ")"]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> 1 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mn> 5 </mn> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[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[TagBox[RowBox[List[TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", 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> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2029052025 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 512 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 512 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 54272 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1247040 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4582800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5143860 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9258030 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 6081075 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 1024 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 107776 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2414400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7467840 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13922460 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 27442665 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 24324300 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 1024 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 108032 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2440576 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7996800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13305960 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 25468110 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 25259985 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </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> </list> <list> <cn type='integer'> 5 </cn> <cn type='integer'> 5 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2029052025 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 512 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 512 </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'> 54272 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1247040 </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'> 4582800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5143860 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9258030 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -6081075 </cn> </apply> <apply> <power /> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1024 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 107776 </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'> 2414400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7467840 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13922460 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 27442665 </cn> <ci> z </ci> </apply> <cn type='integer'> 24324300 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1024 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 108032 </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'> 2440576 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7996800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13305960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25468110 </cn> <ci> z </ci> </apply> <cn type='integer'> 25259985 </cn> </apply> <apply> <power /> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </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["5", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["5", ",", "5"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["512", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6081075"]], "-", RowBox[List["9258030", " ", "z"]], "-", RowBox[List["5143860", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4582800", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1247040", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["54272", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["512", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List["0", ",", SqrtBox["z"]]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["24324300", "+", RowBox[List["27442665", " ", "z"]], "+", RowBox[List["13922460", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7467840", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2414400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["107776", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["1024", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", SqrtBox["z"]]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", SqrtBox["z"]]], "]"]]]], "+", RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List["25259985", "+", RowBox[List["25468110", " ", "z"]], "+", RowBox[List["13305960", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7996800", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2440576", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["108032", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["1024", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List["1", ",", SqrtBox["z"]]], "]"]], "2"]]]]], ")"]]]], RowBox[List["2029052025", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2},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] | |
|
|
|