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http://functions.wolfram.com/03.20.16.0013.01
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KelvinKer[\[Nu], (z^4)^(1/4)] ==
((1/2) z^(-2 + \[Nu]) (z^2 + Sqrt[z^4] + (z^2 - Sqrt[z^4])
Cos[(3 Pi \[Nu])/2]) KelvinKer[\[Nu], z])/(z^4)^(\[Nu]/4) +
((1/2) z^(-2 + \[Nu]) (-z^2 + Sqrt[z^4]) Sin[(3 Pi \[Nu])/2]
KelvinKei[\[Nu], z])/(z^4)^(\[Nu]/4) +
((1/8) Pi z^(-2 - \[Nu]) (2 (z^2 + Sqrt[z^4]) (z^(2 \[Nu]) -
(z^4)^(\[Nu]/2)) + (-z^2 + Sqrt[z^4]) (z^(2 \[Nu]) + (z^4)^(\[Nu]/2))
Sec[(Pi \[Nu])/2]) KelvinBei[\[Nu], z])/(z^4)^(\[Nu]/4) +
((1/8) Pi z^(-2 - \[Nu]) (z^(2 \[Nu]) - (z^4)^(\[Nu]/2))
(2 (z^2 + Sqrt[z^4]) Cot[Pi \[Nu]] + (z^2 - Sqrt[z^4])
Csc[(Pi \[Nu])/2]) KelvinBer[\[Nu], z])/(z^4)^(\[Nu]/4) /;
!Element[\[Nu], Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List["1", "/", "4"]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], "/", "4"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", SqrtBox[SuperscriptBox["z", "4"]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", SqrtBox[SuperscriptBox["z", "4"]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "]"]]]]]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", SqrtBox[SuperscriptBox["z", "4"]]]], ")"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "+", RowBox[List[FractionBox["1", "8"], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], "/", "4"]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", SqrtBox[SuperscriptBox["z", "4"]]]], ")"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]], "-", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List["\[Nu]", "/", "2"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", SqrtBox[SuperscriptBox["z", "4"]]]], ")"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]], "+", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List["\[Nu]", "/", "2"]]]]], ")"]], " ", RowBox[List["Sec", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]]]]]], ")"]], " ", RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "+", RowBox[List[FractionBox["1", "8"], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], "/", "4"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]], "-", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List["\[Nu]", "/", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", SqrtBox[SuperscriptBox["z", "4"]]]], ")"]], " ", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", SqrtBox[SuperscriptBox["z", "4"]]]], ")"]], " ", RowBox[List["Csc", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]]]]]], ")"]], " ", RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Integers"]], "]"]], "]"]]]]]]
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<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> ν </mi> </msub> <mo> ( </mo> <mroot> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mn> 4 </mn> </mroot> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> ν </mi> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msqrt> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ker </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> ν </mi> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </msqrt> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> kei </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> ν </mi> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </msup> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msqrt> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cot </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msqrt> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ber </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> ν </mi> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msqrt> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </msup> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </msqrt> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sec </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> bei </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mtext> </mtext> <mo> /; </mo> <mrow> <mi> ν </mi> <mo> ∉ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> KelvinKer </ci> <ci> ν </ci> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <pi /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> KelvinKer </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <pi /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> KelvinKei </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <pi /> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <cot /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <csc /> <apply> <times /> <pi /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> KelvinBer </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <pi /> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> <apply> <sec /> <apply> <times /> <pi /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> KelvinBei </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <notin /> <ci> ν </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>
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