![](/common/images/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
http://functions.wolfram.com/07.32.03.0120.01
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
HypergeometricPFQRegularized[{}, {1/5, 2/5, 3/5, 4/5}, z] ==
(1/(4 Sqrt[5] Pi^2)) Exp[5 z^(1/5)] + (2/(4 Sqrt[5] Pi^2))
(Exp[((5 (Sqrt[5] - 1))/4) z^(1/5)] Cos[(5/2) Sqrt[(1/2) (5 + Sqrt[5])]
z^(1/5)] + Exp[(-((5 (Sqrt[5] + 1))/4)) z^(1/5)]
Cos[(5/2) Sqrt[(1/2) (5 - Sqrt[5])] z^(1/5)])
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "5"], ",", FractionBox["2", "5"], ",", FractionBox["3", "5"], ",", FractionBox["4", "5"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["4", " ", SqrtBox["5"], " ", SuperscriptBox["\[Pi]", "2"]]]], RowBox[List["Exp", "[", RowBox[List["5", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "+", RowBox[List[FractionBox["2", RowBox[List["4", " ", SqrtBox["5"], " ", SuperscriptBox["\[Pi]", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Exp", "[", RowBox[List[FractionBox[RowBox[List["5", RowBox[List["(", RowBox[List[SqrtBox["5"], "-", "1"]], ")"]]]], "4"], SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]], RowBox[List["Cos", "[", RowBox[List[FractionBox["5", "2"], " ", SqrtBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["5", "+", SqrtBox["5"]]], ")"]]]]], SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["5", RowBox[List["(", RowBox[List[SqrtBox["5"], "+", "1"]], ")"]]]], "4"]]], SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]], RowBox[List["Cos", "[", RowBox[List[FractionBox["5", "2"], " ", SqrtBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["5", "-", SqrtBox["5"]]], ")"]]]]], SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]]]], ")"]]]]]]]]]]
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
<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> 4 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mo>   </mo> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 5 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 2 </mn> <mn> 5 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 5 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 4 </mn> <mn> 5 </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["4", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "5"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["2", "5"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["3", "5"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["4", "5"], 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> <mrow> <mfrac> <mn> 2 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mn> 5 </mn> </msqrt> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> - </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mn> 5 </mn> </msqrt> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQRegularized </ci> <list /> <list> <cn type='rational'> 1 <sep /> 5 </cn> <cn type='rational'> 2 <sep /> 5 </cn> <cn type='rational'> 3 <sep /> 5 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <cn type='rational'> 5 <sep /> 2 </cn> <apply> <power /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <exp /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <cos /> <apply> <times /> <cn type='rational'> 5 <sep /> 2 </cn> <apply> <power /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <exp /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <exp /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/clear.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| | ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "5"], ",", FractionBox["2", "5"], ",", FractionBox["3", "5"], ",", FractionBox["4", "5"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["5", " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]], RowBox[List["4", " ", SqrtBox["5"], " ", SuperscriptBox["\[Pi]", "2"]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", " ", RowBox[List["(", RowBox[List[SqrtBox["5"], "-", "1"]], ")"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["5", "2"], " ", SqrtBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["5", "+", SqrtBox["5"]]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["5", " ", RowBox[List["(", RowBox[List[SqrtBox["5"], "+", "1"]], ")"]]]], ")"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["5", "2"], " ", SqrtBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["5", "-", SqrtBox["5"]]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]]]], ")"]]]], RowBox[List["4", " ", SqrtBox["5"], " ", SuperscriptBox["\[Pi]", "2"]]]]]]]]]] |
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
Date Added to functions.wolfram.com (modification date)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/common/images/spacer.gif) |
|
|