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http://functions.wolfram.com/03.16.06.0004.01
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KelvinKer[z] == (1/2) Sum[((-1 + I)^k/(2^((3 k)/2) k!))
(Sum[Binomial[k, 2 j] (I (1 - I^k) (-2 I (-1)^k Pi
Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]
Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] KelvinBei[-4 j + k,
Subscript[z, 0]] + KelvinKei[4 j - k, Subscript[z, 0]]) +
(1 + I^k) (-2 I (-1)^k Pi Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]
Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] KelvinBer[-4 j + k,
Subscript[z, 0]] + KelvinKer[4 j - k, Subscript[z, 0]])),
{j, 0, Floor[k/2]}] - Sum[Binomial[k, 1 + 2 j]
(I (1 - I^k) (-2 I (-1)^k Pi Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]
Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] KelvinBei[-2 - 4 j + k,
Subscript[z, 0]] + KelvinKei[2 + 4 j - k, Subscript[z, 0]]) +
(1 + I^k) (-2 I (-1)^k Pi Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]
Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] KelvinBer[-2 - 4 j + k,
Subscript[z, 0]] + KelvinKer[2 + 4 j - k, Subscript[z, 0]])),
{j, 0, Floor[(k - 1)/2]}]) (z - Subscript[z, 0])^k, {k, 0, Infinity}]
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Cell[BoxData[RowBox[List[RowBox[List["KelvinKer", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], "k"], " ", SuperscriptBox["2", RowBox[List["-", FractionBox[RowBox[List["3", " ", "k"]], "2"]]]], " "]], RowBox[List["k", "!"]]], RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox["k", "2"], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["k", ",", RowBox[List["2", " ", "j"]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["\[ImaginaryI]", "k"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["z", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "j"]], "+", "k"]], ",", SubscriptBox["z", "0"]]], "]"]]]], "+", RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["4", " ", "j"]], "-", "k"]], ",", SubscriptBox["z", "0"]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ImaginaryI]", "k"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["z", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["KelvinBer", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "j"]], "+", "k"]], ",", SubscriptBox["z", "0"]]], "]"]]]], "+", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["4", " ", "j"]], "-", "k"]], ",", SubscriptBox["z", "0"]]], "]"]]]], ")"]]]]]], ")"]]]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["k", "-", "1"]], "2"], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["k", ",", RowBox[List["1", "+", RowBox[List["2", " ", "j"]]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["\[ImaginaryI]", "k"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["z", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["4", " ", "j"]], "+", "k"]], ",", SubscriptBox["z", "0"]]], "]"]]]], "+", RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List["2", "+", RowBox[List["4", " ", "j"]], "-", "k"]], ",", SubscriptBox["z", "0"]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ImaginaryI]", "k"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["z", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["KelvinBer", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["4", " ", "j"]], "+", "k"]], ",", SubscriptBox["z", "0"]]], "]"]]]], "+", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List["2", "+", RowBox[List["4", " ", "j"]], "-", "k"]], ",", SubscriptBox["z", "0"]]], "]"]]]], ")"]]]]]], ")"]]]]]]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "k"], " "]]]]]]]]]]
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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> <mi> ker </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mi> k </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[RowBox[List["2", " ", "j"]], Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> ⅈ </mi> <mi> k </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> kei </mi> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mi> π </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> bei </mi> <mrow> <mi> k </mi> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> ⅈ </mi> <mi> k </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> ker </mi> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mi> π </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ber </mi> <mrow> <mi> k </mi> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]], Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> ⅈ </mi> <mi> k </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> kei </mi> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mi> π </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> bei </mi> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> ⅈ </mi> <mi> k </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> ker </mi> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mi> π </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ber </mi> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> KelvinKer </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> k </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> k </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <ci> k </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> k </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <imaginaryi /> <ci> k </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> KelvinKei </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <pi /> <apply> <floor /> <apply> <times /> <apply> <arg /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> 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k </ci> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <pi /> <apply> <floor /> <apply> <times /> <apply> <arg /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> KelvinBer </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> k </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <imaginaryi /> <ci> k </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> KelvinKei </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <pi /> <apply> <floor /> <apply> <times /> <apply> <arg /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> KelvinBei </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <ci> j </ci> </apply> <ci> k </ci> <cn type='integer'> -2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <imaginaryi /> <ci> k </ci> </apply> </apply> <apply> <plus /> <apply> <ci> KelvinKer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <pi /> <apply> <floor /> <apply> <times /> <apply> <arg /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> KelvinBer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <ci> j </ci> </apply> <ci> k </ci> <cn type='integer'> -2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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