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http://functions.wolfram.com/03.18.07.0005.01
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KelvinBer[n, z] == (1/Pi) Integrate[Cos[t n + (z Sin[t])/Sqrt[2]]
Cosh[(z Sin[t])/Sqrt[2]], {t, 0, Pi}] /; Element[n, Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "\[Pi]"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List["t", " ", "n"]], "+", FractionBox[RowBox[List["z", " ", RowBox[List["Sin", "[", "t", "]"]]]], SqrtBox["2"]]]], "]"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["z", " ", RowBox[List["Sin", "[", "t", "]"]]]], SqrtBox["2"]], "]"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]
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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> <mrow> <msub> <mi> ber </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> π </mi> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mo> ∫ </mo> <mn> 0 </mn> <mi> π </mi> </msubsup> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mi> t </mi> </mrow> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> KelvinBer </ci> <ci> n </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <pi /> </uplimit> <apply> <times /> <apply> <cos /> <apply> <plus /> <apply> <times /> <ci> n </ci> <ci> t </ci> </apply> <apply> <times /> <ci> z </ci> <apply> <sin /> <ci> t </ci> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <cosh /> <apply> <times /> <ci> z </ci> <apply> <sin /> <ci> t </ci> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBer", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List["t", " ", "n"]], "+", FractionBox[RowBox[List["z", " ", RowBox[List["Sin", "[", "t", "]"]]]], SqrtBox["2"]]]], "]"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["z", " ", RowBox[List["Sin", "[", "t", "]"]]]], SqrtBox["2"]], "]"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Pi]"], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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