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http://functions.wolfram.com/03.17.16.0008.01
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KelvinBei[-\[Nu], z] == (-Sin[Pi \[Nu]]) KelvinBer[\[Nu], z] +
Cos[Pi \[Nu]] KelvinBei[\[Nu], z] + (2/Pi) Sin[Pi \[Nu]] KelvinKei[\[Nu], z]
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Cell[BoxData[RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]", ",", " ", "z"]], "]"]]]], "+", RowBox[List[FractionBox["2", "\[Pi]"], RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", " ", "z"]], "]"]]]]]]]]]]
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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> <msub> <mi> bei </mi> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> bei </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </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> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> π </mi> </mfrac> <mo> ⁢ </mo> <mrow> <msub> <mi> kei </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> KelvinBei </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> <apply> <ci> KelvinBei </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <sin /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> <apply> <ci> KelvinBer </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <sin /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> KelvinKei </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], " ", RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Pi]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
