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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[nu,z] > Transformations > Multiple arguments





http://functions.wolfram.com/03.17.16.0011.01









  


  










Input Form





KelvinBei[\[Nu], Subscript[z, 1] Subscript[z, 2]] == Subscript[z, 1]^\[Nu] Sum[((1 - Subscript[z, 1]^2)^k/k!) (Subscript[z, 2]/2)^k (Sin[(3 k Pi)/4] KelvinBer[\[Nu] + k, Subscript[z, 2]] + Cos[(3 k Pi)/4] KelvinBei[\[Nu] + k, Subscript[z, 2]]), {k, 0, Infinity}] /; Abs[Subscript[z, 2]/Subscript[z, 1]] < 1 || Element[\[Nu], Integers]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]", ",", RowBox[List[SubscriptBox["z", "1"], " ", SubscriptBox["z", "2"]]]]], "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["z", "1", "\[Nu]"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SubsuperscriptBox["z", "1", "2"]]], ")"]], "k"], " "]], RowBox[List["k", "!"]]], SuperscriptBox[RowBox[List["(", FractionBox[SubscriptBox["z", "2"], "2"], ")"]], "k"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "k", " ", "\[Pi]"]], "4"], "]"]], " ", RowBox[List["KelvinBer", "[", RowBox[List[RowBox[List["\[Nu]", "+", "k"]], ",", SubscriptBox["z", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "k", " ", "\[Pi]"]], "4"], "]"]], " ", RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List["\[Nu]", "+", "k"]], ",", SubscriptBox["z", "2"]]], "]"]]]]]], ")"]]]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", FractionBox[SubscriptBox["z", "2"], SubscriptBox["z", "1"]], "]"]], "<", "1"]], "||", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> bei </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msubsup> <mi> z </mi> <mn> 1 </mn> <mi> &#957; </mi> </msubsup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mtext> </mtext> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> bei </mi> <mrow> <mi> k </mi> <mo> + </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <msub> <mi> ber </mi> <mrow> <mi> k </mi> <mo> + </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mfrac> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mfrac> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mi> &#957; </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> KelvinBei </ci> <ci> &#957; </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#957; </ci> </apply> <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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <ci> k </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> k </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> k </ci> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> KelvinBei </ci> <apply> <plus /> <ci> k </ci> <ci> &#957; </ci> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> KelvinBer </ci> <apply> <plus /> <ci> k </ci> <ci> &#957; </ci> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> k </ci> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <or /> <apply> <lt /> <apply> <abs /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <ci> &#957; </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]_", ",", RowBox[List[SubscriptBox["z_", "1"], " ", SubscriptBox["z_", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubsuperscriptBox["zz", "1", "\[Nu]"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SubsuperscriptBox["zz", "1", "2"]]], ")"]], "k"], " ", SuperscriptBox[RowBox[List["(", FractionBox[SubscriptBox["zz", "2"], "2"], ")"]], "k"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "k", " ", "\[Pi]"]], "4"], "]"]], " ", RowBox[List["KelvinBer", "[", RowBox[List[RowBox[List["\[Nu]", "+", "k"]], ",", SubscriptBox["zz", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "k", " ", "\[Pi]"]], "4"], "]"]], " ", RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List["\[Nu]", "+", "k"]], ",", SubscriptBox["zz", "2"]]], "]"]]]]]], ")"]]]], RowBox[List["k", "!"]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", FractionBox[SubscriptBox["zz", "2"], SubscriptBox["zz", "1"]], "]"]], "<", "1"]], "||", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]]]










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





2007-05-02





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