KelvinKer[\[Nu], z] \[Proportional] (-2 I Pi Cos[Pi \[Nu]] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] KelvinBer[-\[Nu], Subscript[z, 0]] + KelvinKer[\[Nu], Subscript[z, 0]] (1/Subscript[z, 0])^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Subscript[z, 0]^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)])) + (1/(2 Sqrt[2])) (2 I Pi Cos[Pi \[Nu]] Floor[Arg[z - Subscript[z, 0]]/ (2 Pi)] Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] (KelvinBei[-1 - \[Nu], Subscript[z, 0]] - KelvinBei[1 - \[Nu], Subscript[z, 0]] + KelvinBer[-1 - \[Nu], Subscript[z, 0]] - KelvinBer[1 - \[Nu], Subscript[z, 0]]) - (1/Subscript[z, 0])^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Subscript[z, 0]^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) (KelvinKei[-1 + \[Nu], Subscript[z, 0]] - KelvinKei[1 + \[Nu], Subscript[z, 0]] + KelvinKer[-1 + \[Nu], Subscript[z, 0]] - KelvinKer[1 + \[Nu], Subscript[z, 0]])) (z - Subscript[z, 0]) - (1/8) (2 I Pi Cos[Pi \[Nu]] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] (KelvinBei[-2 - \[Nu], Subscript[z, 0]] + KelvinBei[2 - \[Nu], Subscript[z, 0]] - 2 KelvinBei[-\[Nu], Subscript[z, 0]]) - (1/Subscript[z, 0])^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Subscript[z, 0]^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) (KelvinKei[-2 + \[Nu], Subscript[z, 0]] - 2 KelvinKei[\[Nu], Subscript[z, 0]] + KelvinKei[2 + \[Nu], Subscript[z, 0]])) (z - Subscript[z, 0])^2 + \[Ellipsis] /; (z -> Subscript[z, 0])

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</mi> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mfrac> <mo> ) </mo> </mrow> <mrow> <mi> &#957; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> arg </mi> <mo> &#8289; </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> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msubsup> <mi> z </mi> <mn> 0 </mn> <mrow> <mi> &#957; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> arg </mi> <mo> &#8289; </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> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </msubsup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> kei </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msub> <mi> kei </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> ker </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msub> <mi> ker </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </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> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> arg </mi> <mo> &#8289; </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> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> bei </mi> <mrow> <mrow> <mo> - </mo> <mi> &#957; 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2007-05-02