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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[nu,z] > Identities > Recurrence identities > Distant neighbors > Decreasing





http://functions.wolfram.com/03.19.17.0010.01









  


  










Input Form





KelvinKei[\[Nu], z] == KelvinKei[-4 + \[Nu], z] + (2 Sqrt[2] (-2 + \[Nu]) (6 + z^2 - 8 \[Nu] + 2 \[Nu]^2) KelvinKei[-3 + \[Nu], z])/z^3 - (4 (-2 + \[Nu]) (-1 + \[Nu]) KelvinKer[-4 + \[Nu], z])/z^2 + (2 Sqrt[2] (-2 + \[Nu]) (-6 + z^2 + 8 \[Nu] - 2 \[Nu]^2) KelvinKer[-3 + \[Nu], z])/z^3










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "4"]], "+", "\[Nu]"]], ",", "z"]], "]"]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["6", "+", SuperscriptBox["z", "2"], "-", RowBox[List["8", " ", "\[Nu]"]], "+", RowBox[List["2", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "3"]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "4"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "2"]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", SuperscriptBox["z", "2"], "+", RowBox[List["8", " ", "\[Nu]"]], "-", RowBox[List["2", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "3"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> kei </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <msub> <mi> kei </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 4 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <mi> kei </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 3 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <mi> ker </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 3 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <mi> ker </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 4 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> KelvinKei </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> KelvinKei </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -4 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> KelvinKei </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -3 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -6 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> KelvinKer </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -3 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> KelvinKer </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "4"]], "+", "\[Nu]"]], ",", "z"]], "]"]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["6", "+", SuperscriptBox["z", "2"], "-", RowBox[List["8", " ", "\[Nu]"]], "+", RowBox[List["2", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "3"]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "4"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "2"]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", SuperscriptBox["z", "2"], "+", RowBox[List["8", " ", "\[Nu]"]], "-", RowBox[List["2", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "3"]]]]]]]]










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





2007-05-02





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