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variants of this functions
KelvinKei




Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/03.15.16.0007.01









  


  








Input Form





KelvinKei[(z^4)^(1/4)] == (1/(4 z^2)) (Pi (-z^2 + Sqrt[z^4]) KelvinBer[z] + Sqrt[z^4] (4 KelvinKei[z] + (4 Log[z] - Log[z^4]) KelvinBei[z]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["KelvinKei", "[", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "4"], ")"]], RowBox[List["1", "/", "4"]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", SqrtBox[SuperscriptBox["z", "4"]]]], ")"]], " ", RowBox[List["KelvinBer", "[", "z", "]"]]]], "+", RowBox[List[SqrtBox[SuperscriptBox["z", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", RowBox[List["KelvinKei", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]], "-", RowBox[List["Log", "[", SuperscriptBox["z", "4"], "]"]]]], ")"]], RowBox[List["KelvinBei", "[", "z", "]"]]]]]], ")"]]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> kei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mroot> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mn> 4 </mn> </mroot> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mfrac> <mrow> <mrow> <msqrt> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> kei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> bei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </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> &#8290; </mo> <mrow> <mi> ber </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> KelvinKei </ci> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> KelvinKei </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <ci> KelvinBei </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <pi /> <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> KelvinBer </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", SuperscriptBox[RowBox[List["(", SuperscriptBox["z_", "4"], ")"]], RowBox[List["1", "/", "4"]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", SqrtBox[SuperscriptBox["z", "4"]]]], ")"]], " ", RowBox[List["KelvinBer", "[", "z", "]"]]]], "+", RowBox[List[SqrtBox[SuperscriptBox["z", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", RowBox[List["KelvinKei", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]], "-", RowBox[List["Log", "[", SuperscriptBox["z", "4"], "]"]]]], ")"]], " ", RowBox[List["KelvinBei", "[", "z", "]"]]]]]], ")"]]]]]], RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]]]]]


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





2007-05-02