Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
KelvinKer






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKer[z] > Series representations > Asymptotic series expansions > Expansions inside Stokes sectors > Expansions containing z->infinity > In trigonometric form ||| In trigonometric form





http://functions.wolfram.com/03.16.06.0020.01









  


  










Input Form





KelvinKer[\[Nu], z] \[Proportional] (Sqrt[Pi]/(E^(z/Sqrt[2]) Sqrt[2 z])) (Cos[(1/8) (Pi (1 + 4 \[Nu]) + 4 Sqrt[2] z)] HypergeometricPFQ[ {(1 - 2 \[Nu])/8, (3 - 2 \[Nu])/8, (5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (1 + 2 \[Nu])/8, (3 + 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8}, {1/4, 1/2, 3/4}, -(16/z^4)] - ((9 - 40 \[Nu]^2 + 16 \[Nu]^4)/(128 z^2)) Sin[(1/8) (Pi (1 + 4 \[Nu]) + 4 Sqrt[2] z)] HypergeometricPFQ[ {(5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (11 - 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8, (11 + 2 \[Nu])/8}, {3/4, 5/4, 3/2}, -(16/z^4)] - ((1 - 4 \[Nu]^2)/(8 z)) Sin[(1/8) (Pi (1 - 4 \[Nu]) - 4 Sqrt[2] z)] HypergeometricPFQ[ {(3 - 2 \[Nu])/8, (5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (3 + 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8}, {1/2, 3/4, 5/4}, -(16/z^4)] + ((225 - 1036 \[Nu]^2 + 560 \[Nu]^4 - 64 \[Nu]^6)/(3072 z^3)) Cos[(1/8) (Pi (1 - 4 \[Nu]) - 4 Sqrt[2] z)] HypergeometricPFQ[ {(7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (11 - 2 \[Nu])/8, (13 - 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8, (11 + 2 \[Nu])/8, (13 + 2 \[Nu])/8}, {5/4, 3/2, 7/4}, -(16/z^4)]) /; (Abs[z] -> Infinity)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]]]], RowBox[List[SqrtBox[RowBox[List["2", "z"]]], " "]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["3", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["1", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["3", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "+", RowBox[List["2", "\[Nu]"]]]], "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["5", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["11", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["11", "+", RowBox[List["2", "\[Nu]"]]]], "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], RowBox[List["8", "z"]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["3", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["3", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "+", RowBox[List["2", "\[Nu]"]]]], "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List["225", "-", RowBox[List["1036", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["560", " ", SuperscriptBox["\[Nu]", "4"]]], "-", RowBox[List["64", " ", SuperscriptBox["\[Nu]", "6"]]]]], RowBox[List["3072", " ", SuperscriptBox["z", "3"]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["7", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["11", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["13", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["11", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["13", "+", RowBox[List["2", "\[Nu]"]]]], "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> ker </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mfrac> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <mi> z </mi> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> </mrow> </msup> </mrow> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 8 </mn> </msub> <msub> <mi> F </mi> <mn> 3 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 16 </mn> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;8&quot;], SubscriptBox[&quot;F&quot;, &quot;3&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;3&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;5&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;7&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;3&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;5&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;7&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;1&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;16&quot;, SuperscriptBox[&quot;z&quot;, &quot;4&quot;]]]], HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 8 </mn> </msub> <msub> <mi> F </mi> <mn> 3 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 16 </mn> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;8&quot;], SubscriptBox[&quot;F&quot;, &quot;3&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;3&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;5&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;7&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;9&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;3&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;5&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;7&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;9&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;1&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;5&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;16&quot;, SuperscriptBox[&quot;z&quot;, &quot;4&quot;]]]], HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 40 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mrow> <mn> 128 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 8 </mn> </msub> <msub> <mi> F </mi> <mn> 3 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 16 </mn> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;8&quot;], SubscriptBox[&quot;F&quot;, &quot;3&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;5&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;7&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;9&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;11&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;5&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;7&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;9&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;11&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;5&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;16&quot;, SuperscriptBox[&quot;z&quot;, &quot;4&quot;]]]], HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 64 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 560 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1036 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 225 </mn> </mrow> <mrow> <mn> 3072 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 8 </mn> </msub> <msub> <mi> F </mi> <mn> 3 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 13 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 16 </mn> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;8&quot;], SubscriptBox[&quot;F&quot;, &quot;3&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;7&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;9&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;11&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;13&quot;, &quot;-&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;7&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;9&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;11&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;8&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;13&quot;]], &quot;)&quot;]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;5&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;7&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;16&quot;, SuperscriptBox[&quot;z&quot;, &quot;4&quot;]]]], HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> KelvinKer </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> </list> <list> <cn type='rational'> 1 <sep /> 4 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <pi /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 9 </cn> </apply> </apply> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 4 </cn> <cn type='rational'> 5 <sep /> 4 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 11 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 11 </cn> </apply> </apply> </list> <list> <cn type='rational'> 3 <sep /> 4 </cn> <cn type='rational'> 5 <sep /> 4 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -64 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 560 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1036 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 225 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 3072 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <pi /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 11 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 13 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 13 </cn> </apply> </apply> </list> <list> <cn type='rational'> 5 <sep /> 4 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 4 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["8", " ", "z"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["225", "-", RowBox[List["1036", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["560", " ", SuperscriptBox["\[Nu]", "4"]]], "-", RowBox[List["64", " ", SuperscriptBox["\[Nu]", "6"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["13", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["13", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["3072", " ", SuperscriptBox["z", "3"]]]]]], ")"]]]], SqrtBox[RowBox[List["2", " ", "z"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02